This paper concerns a problem of robust stabilization of a class of discrete-time systems with norm-bounded parameter uncertainty and unknown constant delay. A new delay-dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities. An algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties. Numerical examples are given to illustrate the proposed results.
This paper concerns delay-dependent guaranteed cost control problem via memoryless state feedback controllers for a class of linear state-delayed systems with normbounded time-varying parametric uncertainties. New delaydependent conditions for the existence of the guaranteed cost controller are presented in terms of matrix inequalities for both nominal state-delayed systems and uncertain state-delayed systems. An algorithm involving convex optimization is proposed to design a controller achieving a suboptimal guaranteed cost such that the system can be stabilized for all admissible uncertainties. Through numerical examples, it is shown that the proposed method can even give the less guaranteed cost than the delay-independent method.
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