LMI Based Tracking Guaranteed Cost Control

This paper addresses the problem of designing the state feedback tracking guaranteed cost controller for a class of norm bounded continuous-time uncertain systems. Firstly, the approach to design a state feedback guaranteed cost controller is presented. The closed-loop system with the designed controller is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality (LMI) design approach, a class of state feedback controller is established, and some sufficient conditions for the existence of guaranteed cost controller are derived. Secondly, the state feedback tracking control law for linear time-invariant system is given. Then combining the guaranteed cost control law with the state feedback tracking control law, the state feedback tracking guaranteed cost control law is proposed. Finally, a specified bank-to-turn (BTT) missile is given as an example, its dynamic model and the linearized model are set up, and the proposed approach is applied to it. The design procedure of the state feedback tracking guaranteed cost controller for the specified BTT missile attitude system is shown. And the six dimensions of freedom simulation results illustrate the effectiveness of the proposed design approach.