The Upper And Lower Bounds For The Solution Of The Continuous Coupled Algebraic Lyapunov Matrix Equation And Its Application

In many fields such as bioengineering and industrial production,the design problems of control systems are involved.The stability,measurability and controllability of the system are important issues that must be considered in the control system and its application research.The discussion of these problems can often be attributed to solving the corresponding Lyapunov matrix equations or estimating the upper and lower bounds of the equations.It is concerned by many control workers and mathematicians,and is one of the research hotspots in control theory.This paper mainly discusses the properties of the solutions of continuous coupled Lyapunov matrix equations generated by complex systems.According to the characteristics of continuous coupling algebra Lyapunov matrix equations and given constraints,construct a semi-positive definite matrix,use the identity of the matrix,according to the relationship between the semi-positive definite solution and the negative definite matrix of the equation,the properties of the non-negative matrix combined with the inequality scaling obtain the upper and lower bounds of the solution of the continuous coupled algebraic Lyapunov matrix equations.The results obtained have improved some of the recent conclusions,and the numerical examples illustrate the superiority.Finally,the upper bounds of the above solutions of continuous coupled algebraic Lyapunov matrix equations are applied to a class of complex control systems,the corresponding Lyapunov functions are designed according to the characteristics of such control systems,then the stability of such control systems is studied.