Robust H<inf>∞</inf> control of uncertain switched delay systems using multiple Lyapunov functions

Abstract

This paper investigates the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control problem for a class of uncertain switched delay systems that involve parameter uncertainties and unknown nonlinear disturbances. Based on the multiple Lyapunov functions method, a sufficient condition for the solvability of the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control problem is derived by employing a hysteresis switching law and variable structure controllers. When the upper bounds of the nonlinear disturbances are unknown, an adaptive variable structure control strategy is developed. The use of adaptive technique is to adapt the unknown upper bounds of the nonlinear disturbances so that the objective of asymptotic stabilization with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -norm bound is achieved under the hysteresis switching law. A numerical example illustrates the effectiveness of the proposed design method.