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

In the design of control system,many important properties,like stability,men-surability,observability of systems often can be converted into studying the proper-ties of the solution of the Lyapunov matrix equation, the upper and lower bounds of the solution and solving the solution.Therefore, many scholars have studied the properties and applications of the algebraic Lyapunov equation, and achieved some important results.Fisrtly,we transforme the matrix equations basing on some matrix inequali-ties and the properties of Lyapunov matrix equations positive definite solution,the upper solution bounds of the continuous algebraic Lyapunov equation are esti-mated and then we apply the result to the stability of a class of control system-s.Secondly,we generalize the result to the upper bounds of the continuous coupled algebraic Lyapunov equation.Main contents as follows: In chapter one, some background knowledge for the continuous algebraic Lyapunov matrix equations, and some basic symbols with definitions are introduced in this paper.In chapter two,we obtain the upper solution bounds by utilizing matrix in-equalities,adding and subtracting itemsin on both sides of the equation,formula transformation and the properties of positive definiteness of real symmetric ma-trix ,meanwhile,we improve some recent results.Then we apply the result to a class of control systems.Further,we give examples to show their effectiveness.In chapter three,on the basis of the upper solution bound of the continuous algebraic Lyapunov equation,by using identical transformation,eigenvalue inequal-ities and the properties of positive definiteness of the continuous coupled algebraic Lyapunov equation,we obtain the new upper bound of the largest eigenvalue esti-mates of the solution bounds of continuous coupled algebraic Lyapunov matrix e-quations.Then by combining the property of M-matrix and nonnegative matrix,we get the upper solution bounds of continuous coupled algebraic Lyapunov matrix equations.