Affine Hybrid Systems

Affine hybrid systems are hybrid systems in which the discrete domains are affine sets and the transition maps between discrete domains are affine transformations. The simple structure of these systems results in interesting geometric properties; one of these is the notion of spatial equivalence. In this paper, a formal framework for describing affine hybrid systems is introduced. As an application, it is proven that every compact hybrid system H is spatially equivalent to a hybrid system H id in which all the transition maps are the identity. An explicit and computable construction for H id is given.

[1]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[2]  Zhendong Sun,et al.  On reachability and stabilization of switched linear systems , 2001, IEEE Trans. Autom. Control..

[3]  Alberto Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 2000, IEEE Trans. Autom. Control..

[4]  M. Jirstrand.  Invariant sets for a class of hybrid systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

[6]  Gene H. Golub,et al.  Matrix computations , 1983 .

[7]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[8]  A. Rantzer,et al.  On the computation of piecewise quadratic Lyapunov functions , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[9]  Lianming Sun,et al.  Output intersampling approach to direct closed-loop identification , 2001, IEEE Trans. Autom. Control..