Analysis And Design For A Class Of Nonlinear Systems Under Communication Constraints

This paper deals with the filter and controller design problems for a class of nonlinearsystems with communication constraints. This kind of nonlinear systems is represented byTakagi-Sugeno (T-S) model fuzzy systems. And the communication constraints consideredhere are information quantization and time-delays. Specifically, the result mainly contains thefollowing three parts:In the first part, the problem of H_∞filtering for a class of discrete-time T-S model nonlinearsystems with quantized signals is addressed. By using a basis-dependent Lyapunov functionapproach, a su?cient condition is firstly provided to ensure the stability of the filtering errorsystem and to guarantee a given H_∞performance level. Based on this analysis result of thefiltering error system and a matrix relaxation technique, a constructive method is proposed forsolving the H_∞filtering problem. A numerical example is also provided to demonstrate thee?ectiveness and merits of the proposed approach.In the second part, the quantized output feedback H_∞controller design problem for a classof discrete-time T-S model fuzzy systems is considered. The measurement output of the systemis quantized by a memoryless logarithmic quantizer before being transmitted to the controller.The problem we address is the design of a full order dynamic output feedback controller ensuringthe asymptotical stability and a prescribed H_∞performance level for the resulting closed-loopsystem. By employing a basis-dependent Lyapunov function approach, we present a su?cientcondition for the solvability of the problem. Then based on this condition, several su?cientconditions for the existence of the desired controller are obtained and the expression of thecontroller is also given. Finally, a numerical example provided demonstrate the e?ectiveness ofthe proposed approach.The third part is concerned with the stability analysis of T-S fuzzy dynamic systems witha constant time-delay. A new delay-dependent asymptotic stability condition for the systemis derived by using a novel quadratic Lyapunov-Krasovskii functional, which is constructed byuniformly dividing the delay interval into multiple segments and choosing proper functionalwith weighted matrices for each segment. It is shown that the result obtained with this ap-proach is less conservative than some other existing results. And a numerical example given also demonstrates the e?ectiveness and merits of the proposed approach.