- Title
- Componentwise ultimate bound and invariant set computation for switched linear systems
- Creator
- Haimovich, H.; Seron, M. M.
- Relation
- Automatica Vol. 46, Issue 11, p. 1897-1901
- Publisher Link
- http://dx.doi.org/10.1016/j.automatica.2010.08.018
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2010
- Description
- 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.
- Subject
- ultimate bounds; invariant sets; switched systems; componentwise methods; solvable Lie algebras
- Identifier
- http://hdl.handle.net/1959.13/923700
- Identifier
- uon:9795
- Identifier
- ISSN:0005-1098
- Language
- eng
- Full Text
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