Index State Observer With Guaranteed Cost Control

In this paper, three problems were investigated. The three problems were respectively construction method of exponential observer for a class of nonlinear systems, the problem of output feedback guaranteed cost control of linear uncertain systems with multiple time-delays and the design methods for resilient guaranteed cost control of linear uncertain systems with multiple time-delays.1 Exponential observer for a class of nonlinear systemsIn this paper, a class of Lipschitz nonlinear systems were discussed. We provided the existing condition of exponential observer for the class of nonlinear systems. Furthermore, we changed sufficient condition to a problem about the solution of a Riccati equation, and we used the solution of the Riccati equation to construct the exponential observer of the class of nonlinear systems that was discussed in this paper.2 The problem of output feedback guaranteed cost control of linear uncertain systems with multiple time-delaysIn this paper, the problem of output feedback guaranteed cost control of linear uncertain systems with multiple time-delays was investigated. At first, we provided the sufficient condition for the existence of output feedback guaranteed cost control. Secondly, we changed sufficient condition to a problem about the positive-definite solution of a matrix inequality. At last, we provided the design method for suboptimal output feedback guaranteed cost control by using the solution of a series of convex optimization problems with LMI constraints.3 The resilient guaranteed cost control of linear uncertain systems with multiple time-delaysThe linear uncertain systems with multiple time-delays that the uncertainties existed both in the systems matrix, and in the controller gain were also investigated. Its investigative design is similar to the investigative design of output feedback guaranteed cost control of linear uncertain systems with multiple time-delays. At first, through considering the definition of guaranteed cost control and the uncertainties in the controller gain, we provided the sufficient condition for the existence of resilient guaranteed cost control. Secondly, we changed sufficient condition to a problem about thepositive-definite solution of a linear matrix inequality. At last, we designed the optimal resilient guaranteed cost controller by using the solution of a convex optimization problems with LM1 constraints.