Reachable Region-Based Filtering of Markov Jump Piecewise-Affine Systems With Bounded Disturbance

This article develops a new filtering strategy for discrete-time Markov jump nonlinear systems approximated via a piecewise-affine (PWA) model. Motivated by the existence of certain partitioned regions that the system state cannot enter within one time step, an algorithm for calculating the reachable target regions for the system state is provided from the currently located region by allowing for bounded disturbance. Then, we analyze the stochastic stability with a desired disturbance-attenuation performance index for the resulting filtering error system (FES) by eliminating all the unreachable regions from target regions at the next time step. In contrast to traditional methods regardless of their unreachable regions, our results can reduce both the computational burden and the conservativeness of the analysis results. In addition, a PWA filter is designed, which excludes all the impossible target regions, such that the FES is stochastically stable, satisfying disturbance-attenuation performance with a lighter computational burden. The validity and advantages of our proposed filtering strategy are verified via a tunnel diode circuit.