Computation of piecewise quadratic Lyapunov functions for hybrid systems

This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. Several examples are included to demonstrate the flexibility and power of the approach.

[1]  T. Pavlidis.  Stability of systems described by differential equations containing impulses , 1967 .

[2]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[3]  John C. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[4]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[5]  Mats Andersson,et al.  Object-Oriented Modeling and Simulation of Hybrid Systems , 1994 .

[6]  M. Corless.  Robust stability analysis and controller design with quadratic Lyapunov functions , 1994 .

[7]  M. Branicky.  Stability of switched and hybrid systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[8]  R. Ortega,et al.  The Semi-Lattice of Piecewise Constant Controls for Non-Linear Systems: A Possible Foundation for Fuzzy Control , 1995 .

[9]  Michael S. Branicky,et al.  Studies in hybrid systems: modeling, analysis, and control , 1996 .

[10]  Bengt LennartsonControl.  Modelling, Analysis & Synthesis of Hybrid Systems , 1996 .

[11]  F. Blanchini,et al.  A new class of universal Lyapunov functions for the control of uncertain linear systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[12]  Kazuo Tanaka,et al.  Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities , 1996, IEEE Trans. Fuzzy Syst..

[13]  Stefan Pettersson.  Modelling, control and stability analysis of hybrid systems , 1996 .

[14]  Michael S. Branicky,et al.  Simulation of Hybrid Systems in Omola/Omsim , 1997 .

[15]  A. Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[16]  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1998, IEEE Trans. Autom. Control..