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<p>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- andby, 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 lined 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.</p>

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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)

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • Y. V. Venkatesh

摘要

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- andby, 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 lined 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.