Asynchronous Static Output-Feedback Control of Markovian Jump Linear Systems

This article aims to study the asynchronous static output-feedback (S-OF) stabilization problem for discrete-time Markovian jump linear systems (MJLSs) with nonideal state and mode detection. Since the system state and mode cannot always be obtained ideally, an asynchronous S-OF controller is designed whose mode can be estimated from the system mode via a hidden Markovian model (HMM). A system augmentation approach is used to obtain an equivalent augmented system, in which the input and (controller gain)-output matrices are separated to facilitate the parameterization of controller gains. Under the augmented system characterization, several new necessary and sufficient stability conditions are established for the concerned closed-loop systems. An iterative LMI-based algorithm is proposed to design an asynchronous S-OF controller. A D-K optimization approach is used to improve its feasibility by finding more appropriate initial values. Three numerical examples are presented to demonstrate the effectiveness of the proposed design methods.