On robust stability of switched linear systems
- Author(s): Nguyen Khoa Son 1 and Le Van Ngoc 2
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View affiliations
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Affiliations:
1:
Institute of Mathematics , Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Rd., Hanoi , Vietnam ;
2: Department of Scientific Fundamentals , Posts and Telecommunications Institute of Technology , Km10 Nguyen Trai Rd, Ha Dong District, Hanoi , Vietnam
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Affiliations:
1:
Institute of Mathematics , Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Rd., Hanoi , Vietnam ;
- Source:
Volume 14, Issue 1,
01
January
2020,
p.
19 – 29
DOI: 10.1049/iet-cta.2019.0144 , Print ISSN 1751-8644, Online ISSN 1751-8652
In this study, the robust stability of continuous-time switched linear systems is investigated under the assumptions that the matrices of the associated linear subsystems are subjected to affine perturbations. The notion of structured stability radius of a switched linear system which is asymptotically exponentially stable w.r.t. arbitrary switchings is introduced. Some lower bounds and upper bounds for estimating this radius are established, by using the system's common quadratic Lyapunov functions and via an approach based on solutions comparison principle. When the nominal switched system is of special structures (for instance when all matrices of subsystems are normal) the obtained bounds yield easily computable formulas for calculating or estimating the system's stability radius. Several examples are provided to illustrate the authors' approach.
Inspec keywords: uncertain systems; discrete time systems; linear systems; continuous time systems; time-varying systems; Lyapunov methods; asymptotic stability; robust control; matrix algebra
Other keywords: quadratic Lyapunov functions; nominal switched system; robust stability; switched linear system; linear subsystems; affine perturbations; asymptotically exponentially stable system; continuous-time switched linear systems; lower bounds; upper bounds; arbitrary switchings; structured stability radius
Subjects: Discrete control systems; Linear control systems; Mathematical analysis; Stability in control theory; Time-varying control systems; Linear algebra (numerical analysis)
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