Generalized Guaranteed Cost Control Under Multi-objective Constraints

With the rapid development of science and technology, all kinds of control systems are more and more complex, and the demand is higher and higher. the multi-objective control has gradually been one of important problems in control field. In the actual control system, takinging into account the inevitable factors, control system will have certain uncertainty. So, when design the control system, the closed-loop system has the robust stability and robust performance, which has important significance and value in the oretical research and practical application.This paper is concerned with the problem of generalized guaranteed cost control for different systems under multiple objective constraints. For a class of generalized cost function, based on Lyapunov theory and linear matrix inequalities(LMI), a condition of the existence is presented. And then a design method is proposed such that the closed-loop system is asymptotically stable and meets some certain performance indicators for all admissible uncertainties.In the paper, we mainly study three parts as follow:(ⅰ) In the first part, for discrete-time systems with Norm-bounded parameter uncertainties and Convex polyhedron uncertainties, the condition for existence and the design method of generalized guaranteed cost control under multiple input and output indicate constraints are studied.(ⅱ) In the second part, for discrete-time systems with Norm-bounded parame-ter uncertainties, the condition for existence and the design method of generalized guaranteed cost control under D-stable and multiple output constraints are stud-ied, the delay-independent conditions for the problem of generalized guaranteed cost control are presented.(ⅲ) In the third part, for a class of delta operator systems with time-delay, the condition for existence and the design method of generalized guaranteed cost control under multiple output constraints are studied.For the presenting design method of generalized guaranteed cost control under multiple constraints, we prove that the method is feasibility by means of example.