This paper investigates the problem of delay-dependent H∞ 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 H∞ 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
Recently, control and synchronization of fractional chaotic systems have increasingly attracted much attention in the fractional control community. In this paper we introduce a novel class of fractional chaotic systems in the pseudo state space and propose an adaptive sliding mode control scheme to stabilize the chaotic systems in the presence of uncertainties and external disturbances whose bounds are unknown. To verify the effectiveness of the proposed adaptive sliding mode control technique, numerical simulations of control design of fractional Lorenz's system and Chen's system are presented.
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