Robust H∞ Control for Discrete-time Singularly Perturbed Systems with Uncertainty and Time-delays

The problem of stability analysis and robust H
∞
control for discrete singularly perturbed systems with uncertainty and time-delay is studied. First, a sufficient condition for the existence of a memory state feedback controller is deduced, which can make the closed-loop system meet the H
∞
performance index requirement. Because the optimal control theory, Moon inequality and other mathematical methods are used in the derivation process, the H
∞
control problem is transformed into a quadratic performance index control problem, which makes the conclusions less conservative. Then, the matrix transformation technique is applied to convert the above conclusions into a MATLAB solvable form, and the parameters of the memory state feedback controller can be obtained by solving the LMI(Linear Matrix Inequality). Finally, a corresponding numerical example is given to verify the effectiveness of the control method.