Structural stability of hybrid systems1

We study hybrid systems from a global geometric perspective as piecewise smooth dynamical systems. Based on an earlier work, we define the notion of the hybrifold as a single piece-wise smooth state space reflecting the dynamics of the original system. Structural stability for hybrid systems is introduced and analyzed in this framework. In particular, it is shown that a Zeno state is locally structurally stable and that a standard equilibrium on the boundary of a domain implies structural instability.

[1]  M. Peixoto,et al.  Structural stability on two-dimensional manifolds☆ , 1962 .

[2]  J. Palis,et al.  Geometric theory of dynamical systems , 1982 .

[3]  L. Tavernini.  Differential automata and their discrete simulators , 1987 .

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

[5]  John Guckenheimer,et al.  Planar Hybrid Systems , 1994, Hybrid Systems.

[6]  Thomas A. Henzinger,et al.  Modularity for Timed and Hybrid Systems , 1997, CONCUR.

[7]  A. Stephen Morse,et al.  Control Using Logic-Based Switching , 1997 .

[8]  A. J. van der Schaft,et al.  Complementarity modeling of hybrid systems , 1998, IEEE Trans. Autom. Control..

[9]  M. Egerstedt,et al.  On the regularization of Zeno hybrid automata , 1999 .

[10]  S. Sastry,et al.  On the existence of executions of hybrid automata , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[11]  Karl Henrik Johansson,et al.  Towards a Geometric Theory of Hybrid Systems , 2000, HSCC.

[12]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[13]  Michael D. Lemmon.  On the Existence of Solutions to Controlled Hybrid Automata , 2000, HSCC.

[14]  Karl Henrik Johansson,et al.  Dynamical Systems Revisited: Hybrid Systems with Zeno Executions , 2000, HSCC.

[15]  C. Pugh,et al.  STRUCTURAL STABILITY OF PIECEWISE SMOOTH SYSTEMS , 2001 .

[16]  B. Dundas,et al.  DIFFERENTIAL TOPOLOGY , 2002 .

[17]  S. Sastry,et al.  HYBRID LIMIT CYCLES AND HYBRID POINCARÉ-BENDIXSON , 2002 .

[18]  Karl Henrik Johansson,et al.  Dynamical properties of hybrid automata , 2003, IEEE Trans. Autom. Control..