Delay-dependent robust H∞ control for with parameter uncertainties and time delay

A delay-dependent sufficient condition for the existence of a robust H_∞ switched controller with state delay feedback for linear switched systems with parameter uncertainties and time delay was derived and formulated in nonlinear matrix inequalities solvable by an iterative algorithm. Compared with the conventional memoryless state-feedback controller, the proposed controller can achieve better robust control performance since the delayed state is utilized as additional feedback information and the parameters of the proposed controllers are changed synchronously with the dynamical characteristic of the system. This design method was also extended to the case where only delayed state is available for the controller. The example of balancing an inverted pendulum on a cart demonstrates the effectiveness and applicability of the proposed design methods.