Robust H<inf>∞</inf> control of Markovian jump systems with mixed time delays

In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results illustrates the effectiveness of the methodology.