ℋ2 filter design through multi-simplex modeling for discrete-time Markov jump linear systems with partly unknown transition probability matrix

This paper is concerned with the ℋ₂ robust filtering problem for discrete-time Markov jump linear systems (MJLS) with transition probability matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the transition probability matrix of MJLS. Full-order filters with partial, complete or null Markov mode observation are synthesized via a linear matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ₂ norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ₂ guaranteed costs when compared to other existing methods.