HMM-based H∞ filtering for discrete-time Markov jump LPV systems over unreliable communication channels

In this paper, the filtering problem is investigated for a class of discrete-time Markov jump linear parameter varying systems with packet dropouts and channel noises in the network surroundings. The partial accessibility of system modes with respect to the designed filter is described by a hidden Markov model (HMM). A typical behavior characterization mechanism is proposed in the communication channel including data losses and additive noises, which occurs in a probabilistic way based on two mutually independent Bernoulli sequences. With the aid of a class of Lyapunov function subject to parameter-dependent and mode-dependent constraints, sufficient conditions ensuring the existence of HMM-based filters are obtained such that the filtering error system is stochastically stable with a guaranteed H∞ error performance. The influence of monotonicity on the performance index is explored while changing the degree of both additive noise and mode inaccessibility. The effectiveness and applicability of the obtained results are finally verified by two numerical examples.