Robust H∞ control of uncertain switched delay systems using multiple Lyapunov functions
Jie Lian, Georgi Marko Dimirovski, Jun Yan Zhao · 2008
This paper investigates the robust Hinfincontrol 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 Hinfincontrol 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 Hinfin-norm bound is achieved under the hysteresis switching law. A numerical example illustrates the effectiveness of the proposed design method.