Robustness of exponential stability of a class of switched positive linear systems with time delays
Summary This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations (FDE) under arbitrary switching or average dwell time switching. We will measure the stability robustness of such a system (which is c...
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| Published in | International journal of robust and nonlinear control Vol. 34; no. 4; pp. 2906 - 2926 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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10.03.2024
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| Abstract | Summary
This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations (FDE) under arbitrary switching or average dwell time switching. We will measure the stability robustness of such a system (which is considered as a nominal system) subject to parameter affine perturbations of its constituent subsystems matrices, by introducing the notion of structured stability radius. Some formulas for computing this radius, as well as estimating its lower bounds and upper bounds, are established. In the case of switched linear systems with multiple discrete time‐delays or/and distributed time‐delays, the obtained results yield tractably computable formulas or bounds for the stability radius. The extension of the obtained results to non‐positive systems and the class of multi‐perturbations has been presented. Examples are given to illustrate the proposed method. |
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| AbstractList | This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations (FDE) under arbitrary switching or average dwell time switching. We will measure the stability robustness of such a system (which is considered as a nominal system) subject to parameter affine perturbations of its constituent subsystems matrices, by introducing the notion of structured stability radius. Some formulas for computing this radius, as well as estimating its lower bounds and upper bounds, are established. In the case of switched linear systems with multiple discrete time‐delays or/and distributed time‐delays, the obtained results yield tractably computable formulas or bounds for the stability radius. The extension of the obtained results to non‐positive systems and the class of multi‐perturbations has been presented. Examples are given to illustrate the proposed method. Summary This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations (FDE) under arbitrary switching or average dwell time switching. We will measure the stability robustness of such a system (which is considered as a nominal system) subject to parameter affine perturbations of its constituent subsystems matrices, by introducing the notion of structured stability radius. Some formulas for computing this radius, as well as estimating its lower bounds and upper bounds, are established. In the case of switched linear systems with multiple discrete time‐delays or/and distributed time‐delays, the obtained results yield tractably computable formulas or bounds for the stability radius. The extension of the obtained results to non‐positive systems and the class of multi‐perturbations has been presented. Examples are given to illustrate the proposed method. |
| Author | Son, Nguyen Khoa Van Ngoc, Le |
| Author_xml | – sequence: 1 givenname: Nguyen Khoa orcidid: 0000-0002-9685-796X surname: Son fullname: Son, Nguyen Khoa email: nkson@vast.vn, nkson1610@gmail.com organization: Vietnam Academy of Science and Technology – sequence: 2 givenname: Le surname: Van Ngoc fullname: Van Ngoc, Le organization: Posts and Telecommunications Institute of Technology |
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This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential... This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations... |
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| SubjectTerms | Differential equations Discrete time systems Dwell time Linear systems Lower bounds Perturbation Robustness robustness of stability stability radius structured perturbations Subsystems switched systems Switching time‐delay systems Upper bounds |
| Title | Robustness of exponential stability of a class of switched positive linear systems with time delays |
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