Petreczky, Mihaly (Centrum voor Wiskunde en Informatica (CWI))

Realization Theory for Discrete-Time Piecewise-Affine Hybrid Systems

Scheduled for presentation during the Regular Session "Hybrid Systems I" (WeA05), Wednesday, July 26, 2006, 11:15−11:40, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 19, 2024

Abstract

The paper investigates the realization problem for piecewise-affine discrete-time hybrid systems. A piecewise-affine discrete-time hybrid system is a discrete-time system such that the state-transition and readout maps are piecewise-affine maps. We will restrict our attention to autonomous systems and we will study the following realization problem. For a specified output trajectory, find a piecewise-affine hybrid system which realizes this output trajectory. We will show that the realization problem for discrete-time piecewise-affine hybrid systems is equivalent to the realization problem for discrete-time switched linear systems. We will give necessary and sufficient conditions for existence of a realization by a discrete-time piecewise-affine and a discrete-time switched linear system. We will also present a procedure for constructing a discrete-time linear switched system and a discrete-time piecewise-affine hybrid system realizing the specified output trajectory.