Analysis for a class of discrete-time switched systems via approximate bisimulations

Abstract

The problem of approximate bisimulations for incrementally stable discrete-time switched systems is investigated. First, a theory of approximation for transition systems with nondeterministic evolution is developed. Then observation metrics are adopted to describe the bounded distance between system observations. Furthermore, a class of Lyapunov-like functions, called bisimulation functions, are utilized to characterize the approximate bisimulation relations. For the class of incrementally stable discrete-time switched systems, the problem of computing bisimulation functions is converted to linear matrix inequalities (LMIs). It is shown that the existence of such bisimulation functions can be guaranteed by the common Lyapunov function or multiple Lyapunov functions of the incrementally stable discrete-time switched systems. A numerical example is finally performed to verify the effectiveness of the achieved approximation bisimulation framework design technique.