Approximately bisimilar symbolic models for incrementally stable switched systems

Switched systems constitute an important modeling para- digm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for a switched system. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e. existence of common or multiple Lyapunov functions), it is possible to construct a symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach we present a realistic example of a boost dc-dc converter and show how to synthesize a switched controller that regulates the output voltage at a desired level. © 2008 Springer-Verlag Berlin Heidelberg.