On the exponential stability and instability analyses of switched second- and higher-order linear systems via a novel application of differential inequalities:part 2(Illustrations)
Y.V.Venkatesh
Abstract：In this second part of the paper, bearing the same title as above, but with the last hyphenated phrase replaced by part 1 (Theory), the exponential stability and instability (ESI) Theorems 1-4 of part 1 are illustrated by applying them to second- and, say, third-order linear switched systems with different eigenvalue structures to demonstrate the versatility, novelty and superiority (over many of the results found in the literature, especially for second-order switched linear systems) of the new theoretical results. The computational procedure that is employed with reference to the third-order systems is generic, in the sense that it is applicable to higher (i.e., greater than third-) order linear switched systems. A pseudo-code for a computer implementation of the stability/instability conditions is also presented. With the principal aim of facilitating an independent reading of this part 2 of the paper, some crucial mathematical notations, definitions and results of part 1 have been repeated, thereby making the contents as self-contained as possible.
Keywords：Differential inequalitiesDwell timeExponential stability and instabilityQuadratic Lyapunov functionsSwitched linear second- and third-(and higher)order systems
Publication Date：2025-12-30
Online Publishing Date：2026-01-09(First online date of this platform, not the publication date of the document)
Pages：29( 721-749 )