Stability of multidimensional linear time-varying systems

Abstract

This paper focuses attention on the stability of multidimensional linear second-order systems with timevarying coefficients. Five theorems on stability and two theorems on instability of such systems and ten corollaries are derived based on Liapunov's second method. Unlike many stability theorems which involve determination of the characteristic equations and their roots, or transformation to a system of first-order equations (thereby often losing sight of the physical parameters of the system), conditions are imposed herein directly on the physical parameters of the system. The theorems derived generalize many existing theorems on the stability of linear constant-coefficient systems.