New results on robust control design of discrete-time uncertain systems

The paper considers the problem of robust control redesign of a class of linear discrete-time systems with norm-bounded parametric uncertainties and controller-gain perturbations. In both cases of additive and multiplicative perturbations, the control objective is to design a resilient feedback-stabilisation schemes using guaranteed cost control and H_∞ control approaches. The problem under consideration is cast as convex optimisation over linear matrix inequalities which led to the derivation of necessary and sufficient conditions for closed-loop robust quadratic stability. Three system examples are provided to illustrate the theoretical developments.