Matrix Bounds For The Solution Of Algebraic Lyapunov Equation Using Delta Operator

Lyapunov equation has important implementation in control theory.The estimation problem of matrix bounds for the unified algebraic Lyapunov equation (UALE) and the continuous algebraic Lyapunov equation (CALE) and the discrete algebraic Lyapunov equation (DALE) could be considered in this paper.The upper and lower matrix bounds for the solution of the unified algebraic Lyapunov equation and the upper and lower matrix bounds and eigenvalue for the solution of the continuous algebraic Lyapunov equation and upper and lower matrix bounds for the solution of the discrete algebraic Lyapunov equation and the lower determinant for the solution of the continuous algebraic Lyapunov equation are presented in terms of matrix inequality approach .The article is composed of four chapters. Chapter one ,we give a short introduction to the theory of the unified algebraic Lyapunov equation (UALE) and the continuous algebraic Lyapunov equation (CALE) and the discrete algebraic Lyapunov equation (DALE) . Chapter two ,in terms of eigenvalue inequality ,the estimation problem of matrix bounds for the unified algebraic Lyapunov equation (UALE) could be considered by unified approach using delta operator. Chapter three,based on the results of chapter two ,the obtained bounds reduced to existing ones for the continuous and discrete Lyapunov equations in the limiting cases . The estimation problem of matrix bounds for the continuous algebraic Lyapunov equation (CALE) and the discrete algebraic Lyapunov equation (DALE) could be considered in this chapter.The proposed results are illustrated through some examples .