Finite-state simulations and bisimulations for discrete-time piecewise affine systems

A procedure for the stability analysis of discrete-time piecewise affine systems is proposed, where a sequence of finite-state symbolic models is constructed such that each of these symbolic models simulates the given piecewise affine system. For a fairly large class of piecewise affine systems, the proposed procedure does not suffer from inherent conservatism, and thus the sequence of symbolic models converges to the original system. For a smaller, restricted class of systems, the sequence of symbolic models is finite, and hence a finite-state bisimulation of the original system is obtained.