Generalized lyapunov equation for the stability analysis of linear time – invariant systems

Abstract

In this paper, a generalized Lyapunov equation is presented to check the behavior of Linear Time-Invariant System, which is used to determine criteria for the stability of the system. The existence of generalized Lyapunov quadratic equation is established and used to study the exponential stability of the system. Illustrative examples have been given to show the effectiveness and the accuracy of the method used.

Keywords: Lyapunov Equation, LTI System Analysis, exponential stability