Componentwise ultimate bound and invariant set computation for switched linear systems

We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form s...

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Bibliographic Details
Published in:Automatica (Oxford) 2010-11, Vol.46 (11), p.1897-1901
Main Authors: Haimovich, H., Seron, M.M.
Format: Article
Language:English
Subjects:
Applied sciences
Componentwise methods
Computation
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Disturbances
Exact sciences and technology
Invariant sets
Invariants
Linear systems
Lyapunov functions
Mathematical analysis
Matrices
Matrix methods
Solvable Lie algebras
Switched systems
Transformations
Ultimate bounds
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Summary:We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2010.08.018