- Title
- Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
- Creator
- Haimovich, Hernan; Braslavsky, Julio H.
- Relation
- IEEE Transactions on Automatic Control Vol. 58, Issue 3, p. 814-820
- Publisher Link
- http://dx.doi.org/10.1109/TAC.2012.2218151
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2013
- Description
- We address the stabilization of switching linear systems (SLSs) with control inputs under arbitrary switching. A sufficient condition for the stability of autonomous (without control inputs) SLSs is that the individual subsystems are stable and the Lie algebra generated by their evolution matrices is solvable. This sufficient condition for stability is known to be extremely restrictive and therefore of very limited applicability. Our main contribution is to show that, in contrast to the autonomous case, when control inputs are present the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices satisfy the aforementioned Lie-algebraic stability condition can become a generic property, hence substantially improving the applicability of such Lie-algebraic techniques in some cases. Since the validity of this Lie-algebraic stability condition implies the existence of a common quadratic Lyapunov function (CQLF) for the SLS, our results yield an analytic sufficient condition for the generic existence of a control CQLF for the SLS.
- Subject
- common quadratic Lyapunov function (CQLF); switching linear systems (SLSs); uniform global exponential stability (UGES)
- Identifier
- http://hdl.handle.net/1959.13/1300007
- Identifier
- uon:19992
- Identifier
- ISSN:0018-9286
- Rights
- © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
- Language
- eng
- Full Text
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