Dissipative filtering for two-dimensional LPV systems: A hidden Markov model approach

In this article, the dissipative filtering problem is explored for two-dimensional (2-D) Markov jump linear parameter varying (MJLPV) systems. The underlying system is described based on the frequently-used Fornasini–Marchesini (FM) model with the measurement missing phenomenon. The hidden Markov model (HMM) is adopted to depict the partial accessibility between system and the designed filter modes. Based on this, a HMM-based filter is proposed, and sufficient conditions in the form of parameterized linear matrix inequalities (PLMIs) are established to guarantee that the filtering error system (FES) is asymptotically stable (AS) and strictly dissipative. Then, the corresponding filter synthesis problem is converted into a convex optimization problem. Ultimately, the simulation example is presented to demonstrate the utility of the obtained results.