Gain scheduled H-infinity control for nonlinear stochastic systems with mixed uncertainties

Abstract

This paper studies the problem of robust gain-scheduled H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller design for a class of nonlinear Markov jump systems with mixed uncertainties, one is time-varying transition probabilities, which follows a nonhomogeneous jump process, and the other one is parameter uncertainty. Nonlinearity of such systems is linearized by means of gradient linearization procedure, and stochastic linear models are constructed in the vicinity of selected operating states, the time varying transition probability matrix is described as a polytope set. By Lyapunov function approach, under the designed controller, a sufficient condition is presented to ensure the resulting closed-loop system is stochastically stable and a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index is satisfied. Finally, continuous gain-scheduled approach is employed to design continuous time-varying controller on the entire nonlinear jump system. A simulation example is given to illustrate the effectiveness of developed techniques.