## Publications

**The papers available here are only drafts, which need not coincide with the published versions**.

**1. THESES**

[A1] P.-A. B.,

*Etude mathématique d’un modèle de frottement sec : le modèle de P.R. Dahl*(

*Mathematical study of P.R. Dahl’s dry friction model*), Thèse de Doctorat en Science, Mathématiques et Automatique, Université Paris IX-Dauphine, March 5th, 1990

[A2] P.-A. B.,

*Mémoire, hystérésis, retards, incertitudes. Quelques résultats de modélisation, d’analyse et de commande*(

*Memory, hysteresis, delays, uncertainties. Some modelling, analysis and control results*), Thèse d’habilitation à diriger des recherches, Université Paris-Sud, November 21st, 2005

2. PAPERS IN INTERNATIONAL JOURNAL WITH LECTURE COMMITTEE

[B1] P.-A. B., Mathematical study of the Dahl’s friction model,

*European J. Mech. A Solids*

**11**no 6 (1992) 835–848

[B2] P.-A. B., A.M. Krasnosel’skii, M. Sorine, A.A. Vladimirov, Nonlinear resonance in systems with hysteresis,

*Nonlinear Analysis, Theory, Methods and Applications*

**27**no 5 (1996) 561–577

[B3] P.-A. B., A.M. Krasnosel’skii, M. Sorine, A.A. Vladimirov, Forced oscillations in control systems with hysteresis,

*Doklady Mathematics*

**53**no 2 (1996) 312-315

[B4] P.-A. B., A.M. Krasnosel’skii, Popov criterion and forced periodic oscillations,

*Automation and Remote Control*

**59**no 4 (1998) 457-466

[B5] M. Akian, P.-A. B., On super-high-frequencies in discontinuous 1sr-order delay-differential equations,

*Journal of Differential Equations*

**162**(2000) 326–358

**[B5.pdf.zip]**

[B6] P.-A. B., Extension of Popov absolute stability criterion to nonautonomous systems with delays,

*International Journal of Control*

**73**no 15, 1349–1361 (2000)

**[B6.pdf.zip]**

[B7] P.-A. B., A.M. Krasnosel’skii, D.I. Rachinskii, Sector estimates of nonlinearities and self-oscillation existence in control systems,

*Automation and Remote Control*

**61**no 6 (2000) 889-903

[B8] P.-A. B., Lyapunov-Krasovskii functionals and frequency domain: delay-independent absolute stability criteria for delay systems,

*International Journal of Robust and Nonlinear Control*

**11**no 8 (2001) 771–788

[B9] P.-A. B., LMI characterization of the strong delay-independent stability of delay systems via quadratic Lyapunov-Krasovskii functionals,

*Systems and Control Letters*

**43**no 4 (2001) 263–274

[B10] P.-A. B., A.M. Krasnosel’skii, D.I. Rachinskii, Strong resonances under Hopf bifurcations in control systems,

*Automation and Remote Control*

**62**no 11 (2001) 1783–1802

[B11] P.-A. B., Stability of nonlinear delay systems: delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method,

*International Journal of Control*

**75**no 4 (2002) 265–274

[B12] M. Akian, P.-A. B., M. Sorine, Control of delay systems with relay,

*IMA Journal on Mathematical Control and Information*

**19**(2002) 133–155

**[B12.pdf.zip]**

[B13] P.-A. B., Lyapunov equation for the stability of 2-D systems,

*Multidimensional Systems and Signal Processing*

**13**no 2 (2002) 201–222

[B14] P.-A. B., Lyapunov equation for the stability of linear delay systems of retarded and neutral type,

*IEEE Trans. Automat. Control*

**47**no 2 (2002) 327–335

**[B14.pdf.zip]**

[B15] P.-A. B., Absolute stability criteria with prescribed decay rate for finite-dimensional and delay systems,

*Automatica*

**38**no 11 (2002) 2015–2019

**[B15.pdf.zip]**

[B16] P.-A. B., A.B. Piunovskiy, M. Sorine, Controlled linear system with delayed relay output under impulse random disturbances,

*Automatica*

**39**no 8 (2003) 1399–1405

[B17] P.-A. B., A convex approach to robust stability for linear systems with uncertain scalar parameters,

*SIAM J. on Control and Optimization*

**42**no 6 (2004) 2016–2042

**[B17.pdf.zip]**

[B18] P.-A. B., An existence result for polynomial solutions of parameter-dependent LMIs,

*Systems and Control Letters*

**51**no 3-4 (2004) 165–169

**[B18.pdf.zip]**

[B19] F. Mazenc, P.-A. B., Backstepping Design for Time-Delay Nonlinear Systems,

*IEEE Trans. Automat. Control*

**51**no 1 (2006) 149–154

**[B19.pdf.zip]**

[B20] P. Tsiotras, P.-A. B., An exact stability analysis test for single-parameter polynomially-dependent linear systems,

*IEEE Trans. Automat. Contro*

*l*

**51**no 7 (2006) 1161–1164

**[B20.pdf.zip]**

[B21] D. Angeli, P.-A. B., Stability of leaderless discrete-time multi-agent systems,

*Mathematics of Control, Signals & Systems*

**18**no 4 (2006) 293–322

**[B21.pdf.zip]**

[B22] P.-A. B., G. Ferrari-Trecate, Average consensus problems in networks of agents with delayed communications,

*Automatica*(accepted)

[B23] P.-A. B., T. Iwasaki, Application of semi-definite programming to robust stability of delay systems,

*Applied Mathematics and Computation*(accepted)

[B24] D. Angeli, P.-A. B., Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees (submitted; a preliminary version may be found here)

[B25] D. Angeli, P.-A. B., Tight estimates for convergence of some non-stationary consensus algorithms (submitted; a preliminary version may be found here)

3. BOOK CHAPTERS

[C1] P.-A. B., M. Sorine, Friction modeling by hysteresis operators. Application to Dahl, sticktion and Stribeck effects,

*in Models of hysteresis*(Trento, 1991), 10–19, Pitman Research Notes in Mathematics Vol. 286, Longman Sci. Tech., Harlow (1993)

[C2] P.-A. B., Extension of Popov criterion to time-varying nonlinearities: LMI, frequential and graphical conditions,

*in Stability and stabilization of nonlinear systems*, D. Aeyels, F. Lamnabhi-Lagarrigue, A. van der Schaft (Eds.), Lecture notes in control and information sciences Vol. 246, Springer-Verlag, Berlin Heidelberg (1999) 95–114

[C3] P.-A. B., Robust absolute stability of delay systems,

*in Nonlinear control in the year 2000*, Vol. 1, F. Lamnabhi-Lagarrigue, A. Isidori, W. Respondek (Eds.), Springer-Verlag (2000) 207–238

[C4] P.-A. B., Root-clustering for multivariate polynomials and robust stability analysis,

*in Unsolved problems in mathematical systems and control theory*, V.D. Blondel, A. Megretski (Eds.), Princeton University Press, Princeton Oxford (2004) 299–303

[C5] P.-A. B., From Lyapunov-Krasovskii Functionals for Delay-Independent Stability to LMI Conditions for μ-Analysis,

*in Advances in Time-Delay Systems*, Lecture Notes in Computational Science and Engineering Vol. 38, Springer, S.-I. Niculescu, K. Gu (Eds.) (2004) 75–88

**[C5.pdf.zip]**

[C6] P.-A. B., Stabilization of LPV Systems,

*in Positive Polynomials in Control*, Lecture Notes in Control and Information Sciences Vol. 312, Springer, D. Henrion, A. Garulli (Eds.) (2005) 103–116

**[C6.pdf.zip]**

4. PAPERS IN PROCEEDINGS OF INTERNATIONAL CONFERENCES WITH LECTURE COMMITTEE

[D1] P.-A. B., L. El Ghaoui, Factorization and smallest-norm roots of multivariable polynomials in robustness analysis,

*Proc. of 30th IEEE CDC*, Brighton (United Kingdom), December 1991

[D2] P.-A. B., M. Sorine, A system theoretic approach of systems with hysteresis. Application to friction modelling and compensation,

*Proc. of 2nd European Control Conference*, Gröningen (Netherlands), 28 June-1 July 1993, 1844–1849

[D3] P.-A. B., M. Sorine, Modelling and control of a class of systems with hysteresis. Application to friction compensation,

*Proc. of IEEE Mediterranean Symposium in New Directions in Control Theory and Applications*, Chania (Greece), 21-23 June 1993

[D4] P.-A. B., M. Sorine, Easy-to-use realistic dry friction models for automatic control,

*Proc. of 3rd European Control Conference*, Roma (Italy), 5-8 Sept. 1995, 3788–3794

**[D4.pdf.zip]**

[D5] P.-A. B., T. Bonald, M. Sorine, Hysteresis Operators and Tyre Friction Models. Application to Vehicle Dynamic Simulation,

*Proc. of ICIAM 95*, Hamburg (Germany), 3-7 July 1995

**[D5.pdf.zip]**

[D6] P.-A. B., A.M. Krasnosel’skii, Periodic solutions of linear systems coupled with relay, in:

*Proceedings of the Second World Congress of Nonlinear Analysts*, Part 2 (Athens, Greece, 1996),

*Nonlinear Analysis, Theory, Methods and Applications*30 (1997), no. 2, 687–696

**[D6.pdf.zip]**

[D7] P.-A. B., M. Sorine, Dry friction models for automatic control,

*Proc. of Euromech Colloquium 351: Systems with Coulomb friction*, Vadstena (Sweden), 5-7 August 1996

**[D7.pdf.zip]**

[D8] P.-A. B., A. Dauron, M. Sorine, Modèles de frottements secs pour les applications embarquées. Application au contact pneu/sol

*Actes des Journées Européennes de Frottement JEF95*, Villeneuve d’Ascq (France), 12-13 Décembre 1995

[D9] D. von Wissel, R. Nikoukhah, F. Delebecque, P.-A. B., M. Sorine, Output trajectory tracking for mechanical systems with dry friction: a DPC approach,

*Proc. of 4th European Control Conference*, Brussels (Belgium), 1-4 July 1997

[D10] K. Aouchiche, P.-A. B., M. Sorine, P.I. control of periodic oscillations of relay systems,

*Proc. of 1st Conf. on Control of Oscillations and Chaos*, St-Petersburg (Russia), 27-29 August 1997

[D11] M. Akian, P.-A. B., M. Sorine, P.I. control of nonlinear oscillations for a system with delay,

*Proc. of 8th IFAC Conf. on Large Scale Systems: Theory and Applications*, Patras (Greece), 15-17 July 1998 [invited]

[D12] M. Akian, P.-A. B., On super-high-frequencies in discontinuous 1sr-order delay-differential equations,

*Proc. of 6th IEEE Mediterranean Conference on Control and Systems*, Alghero (Italy), 9-11 June 1998 [invited]

[D13] P.-A. B., A.M. Krasnosel’skii, Popov-like frequency criterion for existence of forced periodic oscillations,

*Proc. of 37th IEEE CDC*, Tampa (Florida), December 1998

**[D13.pdf.zip]**

[D14] P.-A. B., A.M. Krasnosel’skii, Popov absolute stability criterion for time-varying multivariable nonlinear systems,

*Proc. 5th European Control Conference*, Karlsruhe (Germany), September 1999

[D15] P.-A. B., Delay-independent criterion of absolute stability for nonautonomous systems with variable delays, Modern applied mathematics in circuits, systems and control.

*Proc. of IMACS/IEEE CSCC’99*, Athens (Greece), World Scientific Engineering Society, 300–305 (1999)

[D16] P.-A. B., Absolute stability of nonautonomous delay systems: delay-dependent and delay-independent criteria,

*Proc. of 38th IEEE CDC*, Phoenix (Arizona), December 1999

[D17] P.-A. B., Absolute -stability for rational and delay systems,

*Proc. of 14th Int. Symp. of Mathematical Theory of Networks and Systems MTNS 2000*, Perpignan (France), June 2000

[D18] P.-A. B., Stability of linear delay systems. A note on frequency domain interpretation of Lyapunov-Krasovskii method,

*Proc. of 14th Int. Symp. of Mathematical Theory of Networks and Systems MTNS 2000*, Perpignan (France), June 2000

[D19] P.-A. B., Lyapunov-Krasovskii method and strong delay-independent stability of linear delay systems,

*Proc. of 2nd IFAC Workshop on Linear Time Delay Systems*, Ancona (Italy), September 2000, 5–9

[D20] P.-A. B., Stability criteria for delay systems with sector-bounded nonlinearities,

*Proc. of American Control Conference*, Arlington (Virginia), June 2001

[D21] P.-A. B., S.-I. Niculescu, A note on frequency domain interpretation of Lyapunov-Krasovskii method in control of linear delay systems,

*Proc. of American Control Conference*, Arlington (Virginia), June 2001

[D22] P.-A. B., Bounded-real lemma for 2-D systems. Application to the analysis of delay-independent H1 performance of delay systems,

*Proc. 5th IFAC Symposium “Nonlinear Control Systems” NOLCOS*, St.Petersburg (Russia), July 2001

[D23] P.-A. B., A Lyapunov equation equivalent to internal stability of 2-D systems,

*Proc. of 1st IFAC Symposium on System Structure and Control*, Prague (Czech Republic), August 2001

[D24] P.-A. B., Solvability of a Lyapunov equation for characterization of asymptotic stability of linear delay systems,

*Proc. of 6th European Control Conf*., Porto (Portugal), September 2001

[D25] P.-A. B., Delay-independent small gain theorem and frequency domain interpretation of the Lyapunov- Krasovskii method for stability of nonlinear delay systems,

*Proc. of 6th European Control Conf*., Porto (Portugal), September 2001

[D26] P.-A. B., Nonconservative LMI criteria for delay-independent stability of delay systems, based on quadratic Lyapunov-Krasovskii functionals,

*Proc. of 40th IEEE CDC*, Orlando (Florida), December 2001

[D27] P.-A. B., LMI approach to spectral stabilizability of linear delay systems, and stabilizability of linear systems with complex parameter

*Proc. of 40th IEEE CDC*, Orlando (Florida), December 2001

[D28] P.-A. B., Delay-independent circle criterion and Popov criterion,

*Proc. of 3rd IFAC Workshop on Time Delay Systems*, Santa Fe (New Mexico), December 2001

[D29] P.-A. B., A.B. Piunovskiy, M. Sorine, Optimal control of stochastic linear system with delayed relay output,

*Proc. of 15th IFAC World Congress*, Barcelona (Spain), July 2002

[D30] P.-A. B., Root location of multivariable polynomials and stability analysis, Open problem book,

*in Proc. of 15th Int. Symp. of Mathematical Theory of Networks and Systems MTNS 2002*, University of Notre-Dame (Indiana), August 2002.

[D31] P.-A. B., Nonconservative LMI approach to robust stability for systems with uncertain scalar parameters,

*Proc. of 41st IEEE CDC*, Las Vegas (Nevada), December 2002

[D32] P.-A. B., LMIs for delay-independent properties of delay systems and input-output analysis of systems with complex parameter,

*Proc. of 41st IEEE CDC*, Las Vegas (Nevada), December 2002

[D33] P.-A. B., G. Ferrari-Trecate, Stability analysis of discrete-time switched systems through Lyapunov functions with nonminimal state,

*Proc. of IFAC Conf. on Analysis and Design of Hybrid Systems ADHS03*, St-Malo (France), June 2003

**[D33.pdf.zip]**

[D34] P.-A. B., Stabilization of LPV systems,

*Proc. of 42nd IEEE CDC*, Maui (Hawai), December 2003

**[D34.pdf.zip]**

[D35] P.-A. B., F. Mazenc, Backstepping design for time-delay nonlinear systems,

*Proc. of 42nd IEEE CDC*, Maui (Hawai), December 2003

**[D35.pdf.zip]**

[D36] P.-A. B., C. Prieur, On existence of smooth solutions of parameter-dependent convex programming problems,

*Proc. of 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS2004),*Leuven (Belgium), July 2004

**[D36.pdf.zip]**

[D37] P.-A. B., On robust semidefinite programming,

*Proc. of 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS2004),*Leuven (Belgium), July 2004

**[D37.pdf.zip]**

[D38] P. Tsiotras, P.-A. B., An exact stability test for one-parameter polynomially-dependent linear systems,

*Proc. of 43rd IEEE CDC*(Bahamas), December 2004

**[D38.pdf.zip]**

[D39] X. Zhang, P. Tsiotras, P.-A. B., Multi-Parameter Dependent Lyapunov Functions for the Stability Analysis of Parameter-Dependent LTI Systems,

*Proc. of 13th Mediterranean Conference on Control and Automation*, Limassol (Cyprus), June 2005

**[D39.pdf.zip]**

[D40] D. Angeli, P.-A. B., Extension of a result by Moreau on stability of leaderless multi-agent systems,

*Proc. of 44th IEEE CDC*, Sevilla (Spain), December 2005

**[D40.pdf.zip]**

[D41] P.-A. B., G. Ferrari-Trecate Average consensus problems in networks of agents with delayed communications,

*Proc. of 44th IEEE CDC*, Sevilla (Spain), December 2005

**[D41.pdf.zip]**

[D42] P.-A. B., T. Iwasaki, LMI characterisation of robust stability for time-delay systems: singular perturbation approach,

*Proc. of 45th IEEE CDC*, San Diego (California), December 2006

**[D42.pdf.zip]**

[D43] P.-A. B., R.C.L.F. Oliveira, V.F. Montagner, P.L.D. Peres, Existence of homogeneous polynomial solutions for parameter-dependent Linear Matrix Inequalities with parameters in the simplex,

*Proc. of 45th IEEE CDC*, San Diego (California), December 2006

**[D43.pdf.zip]**

[D44] R.C.L.F. Oliveira, V.F. Montagner, P.L.D. Peres, P.-A. B., LMI relaxations for H-infinity control of time-varying polytopic systems by means of parameter-dependent quadratically stabilizing gains,

*Proc. of 3rd IFAC Symposium on System, Structure and Control (SSSC07),*Foz do Iguaçu (Brazil), October 2007

[D45] M.M. Peet, P.-A. B., An Extension of the Weierstrass Theorem to Linear Varieties: Application to Delay Systems, Proc. of 7th IFAC Workshop on Time--Delay Systems (TDS07), Nantes (France), September 2007

5. PAPERS IN PROCEEDINGS OF NATIONAL CONFERENCES WITH LECTURE COMMITTEE

[E1] P.-A. B., R.C.L.F. Oliveira, V.F. Montagner, P.L.D. Peres, Existência de soluções polinomiais homogêneas para desigualdades matriciais lineares com parámetros no simplex,

*Proc. XVI Congresso Brasileiro de Automática,*Salvador (Bahia), October 2006

6. RESEARCH REPORTS

[F1] P.-A. B., A.M. Krasnosel’skii, M. Sorine, A.A. Vladimirov, Nonlinear resonance in systems with hysteresis,

**INRIA Research report 2689**, 1995

[F2] P.-A. B., A.M. Krasnosel’skii, M. Sorine, Dither in systems with hysteresis,

**INRIA Research report 2690**, 1995

[F3] M. Akian, P.-A. B., M. Sorine, P.I. control of nonlinear oscillations for a system with delay,

**INRIA Research report 3422**, 1998

[F4] M. Akian, P.-A. B., On super-high-frequencies in discontinuous 1st-order delay-differential equations,

**INRIA Research report 3443**, 1998

[F5] P.-A. B., A.M. Krasnosel’skii, An extension of Popov criterion to multivariable time-varying nonlinear systems. Application to criterion for existence of stable limit cycles,

**INRIA Research report 3512**, 1998

[F6] P.-A. B., Extension of Popov absolute stability criterion to nonautonomous systems with delays,

**INRIA Research report 3625**, 1999

[F7] P.-A. B., A.M. Krasnosel’skii, D.I. Rachinskii, Sector Estimates of Nonlinearities and Existence of Cycles in Control Systems, Institute for Nonlinear Sciences, National University of Ireland, University College, Cork,

**report 00-002**(March 2000)

[F8] P.-A. B., LMI characterization of the strong delay-independent stability of delay systems via quadratic Lyapunov-Krasovskii functionals,

**Report research no 3968**, INRIA (July 2000)

[F9] P.-A. B., Stability of nonlinear delay systems: delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method,

**Report research no 3969**, INRIA (July 2000)

[F10] P.-A. B., Lyapunov equation for the stability of 2-D systems,

**Report research no 4014**, INRIA (September 2000)

[F11] P.-A. B., Lyapunov equation for the stability of linear delay systems of retarded and neutral type,

**Report research no 4127**, INRIA (March 2001)

[F12] P.-A. B., Nonconservative LMI criteria for characterization of delay-independent properties of delay systems. Application to stability and input-output analysis of systems with complex parameter,

**Report research no 4278**, INRIA (October 2001)

[F13] P.-A. B., A convex approach to robust stability for linear systems with uncertain scalar parameters,

**Report research no 4316**, INRIA (November 2001)

[F14] P.-A. B., A.B. Piunovskiy, M. Sorine, A controlled linear system with relay output under impulse random disturbances, Transactions of the French-Russian A.M. Liapunov Institute for Applied Mathematics and Computer Science, vol. 2, Moscow, Russia (2001), 113–126.

[F15] P.-A. B., An existence result for polynomial solutions of parameter-dependent LMIs,

**Report research no 4798**, INRIA (April 2003)

[F16] P.-A. B., On Positiveness of Matrix-Valued Polynomials and Robust Semidefinite Programming,

**Report research no 4906**, INRIA (August 2003)

[F17] P.-A. B., Existence of polynomial solutions to robust convex programming problems,

**Report research no 4910**, INRIA (August 2003)

[F18] D. Angeli, P.-A. B., Stability of leaderless multi-agent systems. Extension of a result by Moreau,

**http://arxiv.org/abs/math.OC/0411338**(November 2004)

[F19] P.-A. B., G. Ferrari-Trecate, Average consensus problems in networks of agents with delayed communications,

**http://arxiv.org/abs/math.OC/0503009**(March 2005)

[F20] D. Angeli, P.-A. B., Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees,

**http://arxiv.org/abs/math.OC/0610854**(October 2006)

[F21] D. Angeli, P.-A. B., Tight estimates for convergence of some non-stationary consensus algorithms,

**http://arxiv.org/abs/0706.0630**(June 2007)