Asynchronous Quantized $H_{\infty}$ Filtering of Singular Nonhomogeneous Markov Jump Systems

This paper presents an approach for designing asynchronous quantized <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> filter for discrete-time singular nonhomogeneous Markov jump systems (NMJSs). The study addresses systems with time-varying transition probabilities modeled via polytopic sets, and investigates asynchronous characteristics among system, quantizer, and filter modes through the application of hidden Markov models (HMMs). A polyhedral Lyapunov function is constructed and a sector bound approach is adopted for quantized error processing, we derive the regularity, causality, and stochastic stability of the filter error system, along with the satisfaction of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance constraints. By introducing slack matrices and variable substitutions, nonlinear matrix inequalities are transformed into solvable linear matrix inequality (LMI) forms, ultimately enabling the derivation of filter gains. Lastly, the proposed methodology is validated through a tunnel diode circuit, demonstrating its effectiveness in achieving stochastic admissibility and desired <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance.