A note on quadratic performance of a class of switched uncertain nonlinear systems
We address quadratic performance, specifically quadratic stabilization and [Formula: see text] gain for a class of switched systems consisting of uncertain nonlinear subsystems. In each subsystem, there exist norm-bounded uncertainty and constant vector in the linear part, and the vector field inclu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2024-12-01
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| Series: | Systems Science & Control Engineering |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/21642583.2024.2395405 |
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| Summary: | We address quadratic performance, specifically quadratic stabilization and [Formula: see text] gain for a class of switched systems consisting of uncertain nonlinear subsystems. In each subsystem, there exist norm-bounded uncertainty and constant vector in the linear part, and the vector field includes a nonlinear term with a quadratic constraint. Under the assumption that a convex combination of subsystems' constant vectors reaches the origin, we define a new convex combination of subsystems (CCS) without a constant vector, which incorporates the system matrices, uncertainties and nonlinear terms in a unified manner. If the CCS is quadratically stable (QS) at the origin, we propose a state-dependent switching law under which the switched uncertain nonlinear system (SUNS) is also QS at the origin. A detailed discussion is also presented on the upper bound of the system state when the convex combination of the subsystems' constant vectors is not zero. Furthermore, a parallel discussion and results are established for the quadratic [Formula: see text] gain of the SUNS. |
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| ISSN: | 2164-2583 |