Piecewise Homogeneous-Type Stabilization for Nonlinear Semi-Markov Jump Systems: Controller Design and Experiments

This article investigates the mean-square stabilization problem of nonlinear semi-Markov jump systems (SMJSs) subject to time-varying transition rates (TRs). To accommodate TRs variations across different operating conditions, a piecewise homogeneous embedded Markov chain (EMC), varying across intervals but time-invariant within each interval, is introduced. Considering partial states unobservability and real-time requirements, a mode-dependent fuzzy dynamic output feedback controller is developed, operating across multiple homogeneous Markov chain levels for real-time performance control. By incorporating richer sojourn-time information and membership function (MF) characteristics, elapsed-time term and the homogeneous polynomially parameter-dependent (HPPD) method are integrated into Lyapunov functions (LFs), enabling relaxed stability conditions. Furthermore, different utilization efficiencies of available semi-Markov kernel (SMK) information are discussed, with extended exploitation of partial information covering existing conservative results. Finally, numerical simulations of a tunnel diode circuit model (TDCM) and hardware-in-the-loop (HIL) tests of a suspension system are presented to demonstrate the superior control performance of the proposed method compared to existing methods.