Nonsynchronized State Estimation for Fuzzy Markov Jump Affine Systems With Switching Region Partitions

This article investigates the state estimation issue of discrete-time Takagi–Sugeno fuzzy Markov jump affine systems that cover both traditional fuzzy Markov jump systems and fuzzy affine systems as two special cases. The original system is transformed into a Markov jump piecewise-affine system that varies with different operating regions. The fuzzy rules are dependent on the system mode, and accordingly, the partition of the state space is mode dependent. To analyze the stochastic stability of the estimation error system, a novel mode-dependent piecewise Lyapunov function is constructed, in which the region indices of both the plant state and the estimator state are mode dependent. Then, the existence for a simultaneously mode-dependent and region-dependent fuzzy affine estimator is investigated by virtue of the
$\mathcal {S}$
-procedure and ellipsoidal outer approximation such that the estimation error system is stochastically stable with a prescribed
$\mathcal { H}_{\infty }$
performance. In the end, an illustrative example of a tunnel diode circuit is adopted to showcase the effectiveness and practicability of the developed state estimation strategy.