Polynomial-Based Gain-Scheduling Mechanism of Fuzzy Markov Jump System With Incomplete Transition Probability Information With Experimental Validation

This article investigates the stabilization problem of fuzzy Markov jump systems (F-MJSs) with incomplete transition probability (TP) information. Existing methods for handling partially unknown TPs often introduce excessive conservatism using scaling techniques that may violate the fundamental stochastic constraints. To address this issue, we propose a novel polynomial-based gain-scheduling control framework that integrates a polytopic probability reconstruction strategy. This strategy rigorously preserves the stochastic completeness of TP matrices (TPMs) while reducing conservatism in controller design. By leveraging homogeneous polynomial theory, we further establish a codesign methodology for both polynomial Lyapunov functions and fuzzy controllers, significantly expanding the feasible solution space. Theoretical analysis demonstrates that the proposed method achieves substantially reduced conservatism compared with conventional aggregated approximation approaches. Numerical simulations reveal the improvement compared with classical aggregated treatment approaches. Hardware-in-the-loop (HIL) experiments on active suspension systems validate the effectiveness and robustness of the designed control strategy, especially γ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/><roman xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</roman> achieved a reduction optimization of 87.5%.