H∞ control of markovian switching systems with time-delays: Applied to DC-DC converters

The DC-DC switching power converters are highly nonlinear systems. Consequently, the conventional linear controls based on averaging and linearization techniques will result in poor dynamic performance or system instability. In order to resolve this problem, in this paper a robust state feedback H∞ control is proposed for these systems under Markovian switching with mixed discrete, neutral and distributed delays. Based on the Lyapunov-Krasovskii functional theory, some required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired control is derived based on a convex optimization method.