New Method to Derive Stability Intervals of Symmetric System Matrices with Multiple Uncertain Parameters Using the Generalized Stability Feeler

Abstract

In this paper we present a new method for stability analysis of a class of nonlinear systems. We assume that the nonlinear system can be considered as a linear system with multiple uncertain parameters, of which system matrix is symmetric. Our proposed method enables one to derive complete intervals of an uncertain parameter which stabilize the considered system. The proposed method is based on the generalized stability feeler and the extreme point result for symmetric matrices. The generalized stability feeler is a tool for system matrices with single uncertain parameter. By using the generalized stability feeler, we can derive stability intervals of system matrices with single uncertain parameter. In order to derive stability intervals of system matrices with multiple uncertain parameters, we use not only the generalized stability feeler, but also the extreme point result for symmetric matrices. By using them, a new theorem is derived, which can be used to derive the stability intervals of the considered system.