A singular system approach to robust and non-fragile filtering design for continuous-time semi-Markovian jump systems

This paper proposes a singular system approach to robust and non-fragile ℋ_∞ filtering design for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs) with norm-bounded uncertainties. By a singular model transformation approach and a semi-Markovian Lyapunov function, a sufficient condition for robust ℋ_∞ performance analysis is firstly derived and then the non-fragile filter synthesis is developed. It is shown that by a linearisation technique combined with sojourn-time partitioning idea, a unified framework can be developed such that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities. Finally, simulation studies are provided to illustrate the effectiveness of the proposed method.