The robust stability of control systems with perturbation is considered. Usin 9 L yapunov functions, quantitative bounds on the perturbation are obtained such that the systems remain stable. Four classes of perturbations are treated and four measures of robust stability are proposed: the nondelay unstructured, delayed unstructured, nondelay structured, and delayed structured measures. Examples are given, and comparisons with the results given in current literature are made.
Nomenclature
real n-dimensional vector space linear operators from ~" to R" inverse matrix of an invertible matrix [-] transposed matrix of ['] square-root of positive-definite matrix [.] symmetric portion of square matrix [-] positive-semidefinite matrix formed by replacing each eigenvalue of the symmetric matrix [.] by its modulus value maximum singular value of matrix [.] minimum singular value of matrix [.] Euclidean norm of vector v square symmetric matrix P being positive-definite square symmetric matrices P and Q that satisfy P-Q > 0
L Introduction
The inclusion of plant uncertainty and parameter variations to the analysis and design of control systems has been an important problem. The uncertainty, described as unstructured perturbation, often arises from an imperfect knowledge of a system working at the presence of noise and disturbance. The parameter variations, described as structured perturbations, arise if a system is operated in