Abstract
In this paper, the problems of stability and stabilization for a class of discrete-time Markov jump nonlinear systems are investigated, where the nonlinearities are approximated by piecewise-affine (PWA) dynamics. The proposed system is general as it can cover both the conventional Markov jump linear system and PWA systems as special cases. A concept of admissible adjacent switching paths (AASPs) set is proposed to reduce the conservatism of stability analysis, paralleling to the region switching pairs in the context of conventional PWA systems. A simultaneous mode-dependent and region-dependent affine controller is designed based on a S-procedure of using ellipsoidal outer approximation such that the closed-loop system is stochastically stable. A numerical example is given to illustrate the effectiveness and potential of the developed theoretical results.
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