Generalised nonlinear l2–l∞ filtering of discrete-time Markov jump descriptor systems

This paper is devoted to the l2–l∞ filter design problem for nonlinear discrete-time Markov jump descriptor systems subject to partially unknown transition probabilities. The partially unknown transition probabilities are modelled via the polytopic uncertainties. The objective is to propose a generalised nonlinear full-order filter design method, such that the resulting filtering error system is regular, casual, and stochastically stable, and a prescribed l2–l∞ attenuation level is satisfied. For the autonomous discrete-time descriptor system subject to Lipschitz nonlinear condition, by introducing some slack matrix variables, a mode-dependent stability criterion is established. It cannot only ensure the regularity, casuality, and stochastic stability of system, but also guarantee the considered system has a unique solution. Based on this obtained criterion, a sufficient condition in terms of linear matrix inequalities (LMIs) is derived, such that the resulting filtering error system is regular, casual, stochastically stable while satisfying a given l2–l∞ performance index. Further, the nonlinear mode-dependent l2–l∞ filter design method is proposed, and by solving a set of LMIs, the desired filter gain matrices are also explicitly given. Finally, a numerical example is included to illustrate the effectiveness of our proposed approach.