Finite-time passive control for interval energy-storing electrical circuit model with time-delay and Markov switching

Abstract

In this paper, we focus on the stochastic finite-time passive control problem for interval energy-storing electrical systems with time-delay and Markov switching. The mathematical model of energy-storing electrical circuit is given firstly, in which not only the error of resistor R, inductance L and capacitor C, but the stochastic disturbance as well are considered. To investigate the finite-time passive control for the interval energy-storing electrical circuit, mathematical model is transformed into a kind of stochastic uncertain systems with time-delay and Markov switching. By constructing a Lyapunov-Krasovskii functional, together with linear matrix inequalities (LMIs) toolbox, some sufficient conditions are given. Meanwhile, the passive controllers are also designed by solving the corresponding LMIs. Naturally, a numerical examples with simulation is given to illustrate the correctness and effectiveness of the designed controller.