A Novel Memory Filtering Design for Semi-Markovian Jump Time-Delay Systems

This paper investigates the problem of delay-dependent <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mathscr {H}_{\infty }}$ </tex-math></inline-formula> memory filtering for continuous-time semi-Markovian jump linear systems (MJLSs) with time-varying delay in an input-output framework. Differing from the constant transition rates (TRs) in the conventional MJLSs, the TRs of the semi-MJLSs depend on the random sojourn-time and are thus with time-varying characteristics. By utilizing a two-term approximation for the terms with time-varying delay, it is first shown that the filtering error system (FES) can be reformulated into a feedback interconnection form and the stability and performance analysis problem of the FES can be recast as the scaled small gain (SSG) problem of an interconnected system. Then, based on a semi-Markovian Lyapunov–Krasovskii formulation of SSG condition combined with projection lemma, the <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mathscr {H}_{\infty }}$ </tex-math></inline-formula> filter synthesis for the underlying semi-MJLSs is formulated in terms of linear matrix inequalities. Finally, simulation studies are provided to evaluate the effectiveness and superiority of the proposed design method.