Optimal Guaranteed Cost Control for Discrete Time Uncertain Time-Delay Systems with Control Input Constraints
具有控制约束的不确定离散时滞系统最优保性能控制

For a class of discrete-time state delay systems with norm-bounded time-varying parameter uncertainty and control input constraints, this paper addresses the problem of designing an optimal guaranteed cost state feedback controller. A condition for the existence of guaranteed cost controllers is derived. Furthermore, it is shown that this condition is equivalent to the feasibility problem of a certain linear matrix inequality system, and its solutions provide a parametrized representation of guaranteed cost controllers. Based on that fact, the design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques. Finally, an example is given to illustrate the proposed results.