Design Of Time-delay Continuous Nonlinear Systems Based On Lyapunov Matrices

This paper mainly studies the guaranteed cost control problem and practical stability analysis problem of delayed continuous-time nonlinear systems based on Lyapunov matrix.The main contents are as follows:First,the guaranteed cost control problem for a class of delayed continuous–time nonlinear systems is studied.Firstly,we introduced the definition and related properties of Lyapunov matrix.Secondly,by constructing a Lyapunov–Krasovskii(L–K)functional based on Lyapunov matrix,a new method for designing stabilization controllers and guaranteed cost controllers is proposed.In addition,the sufficient conditions for the existence of stabilization controllers and guaranteed cost controllers based on linear matrix inequality are investigated,which make the closed-loop system to be stable and its cost function to have an upper bound.Finally,two numerical examples are given to verify the effectiveness of the proposed method.Second,the globally robust practical exponential r-stability criterion for a class of delayed continuous-time nonlinear systems is given.Firstly,based on Lyapunov matrix,a new L–K functional is constructed,and thereby,a new method is proposed to establish the globally robust practical exponential r-stability criterion for delayed continuous-time nonlinear systems.In addition,the practical stabilization controller for the three-state diesel engine model is designed using the proposed stability criterion,and a good control effect is obtained.