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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) |
| Y.V.Venkatesh1,2 |
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| (1 (Formerly) Division of Electrical Sciences, Indian Institute of Science, Sir C. V. Raman Road, Bangalore 560012, Karnataka, India
2 Department of Electrical and Computer Engineering, National University of Singapore, Kent Ridge Crescent, Singapore 119260, Singapore) |
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| 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 secondandby,
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. |
| 关键词: Differential inequalities · Dwell time · Exponential stability and instability · Quadratic Lyapunov functions · Switched linear second- and third- (and higher) order systems |
| DOI：https://doi.org/10.1007/s11768-025-00246-w |
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| 基金项目: |
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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) |
| Y. V. Venkatesh1,2 |
| (1 (Formerly) Division of Electrical Sciences, Indian Institute of Science, Sir C. V. Raman Road, Bangalore 560012, Karnataka, India
2 Department of Electrical and Computer Engineering, National University of Singapore, Kent Ridge Crescent, Singapore 119260, Singapore) |
| 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 secondandby,
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. |
| Key words: Differential inequalities · Dwell time · Exponential stability and instability · Quadratic Lyapunov functions · Switched linear second- and third- (and higher) order systems |
