Mixed H∞ and passive control for singular Markovian jump systems with time delays

This paper addresses the problem of admissibility analysis, and mixed H∞ and passive control synthesis for a class of singular systems with Markovian jumps and time delays. By implementing an appropriate Lyapunov-Krasovskii functional together with Wirtinger-based inequality, a new set of delay dependent sufficient condition is derived in terms of linear matrix inequalities which guarantees that the singular Markovian jump system is regular, impulse-free and stochastically stable. In particular, the delay factor is assumed to be either constant or time varying, and either differentiable or non-differentiable. Also, it is noted that the proposed stochastic admissibility criteria are delay dependent in general and delay derivative dependent when the delay is differentiable. Further, mixed H∞ and passive control design with an appropriate gain matrix has been derived to achieve the stabilization for singular systems in the presence of differentiable as well as non-differentiable time varying delays. More precisely, when the proposed LMIs are feasible, an expression for a desired mixed H∞ and passive control will be determined. Also, as special cases different control systems such as H∞ and passivity control process can be achieved for the considered systems with the proposed design procedure. Finally, several numerical examples including DC motor driving model are given to verify the effectiveness of the proposed design technique.