Conditions for uniform solvability of parameter-dependent Lyapunov equations with applications

P. Krishnamurthy, Farshad Khorrami

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of finding a common quadratic Lyapunov function to demonstrate stability of a family of matrices which incorporate design freedoms. Generically, this can be viewed as picking a family of controller (or observer) gains so that the family of closed-loop system matrices admit a common Lyapunov function. We provide several conditions, necessary and sufficient, for various structures of matrix families. Families of matrices containing a subset of diagonal matrices invariant under the design freedoms is also considered since this is a case that occurs in many applications. Conditions for uniform solvability of the Lyapunov equations are explicitly given and involve inequalities regarding relative magnitudes of terms in the matrices. Motivating applications of the obtained results to observer and controller designs for time-varying, switched, and nonlinear systems are highlighted.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
Pages3896-3901
Number of pages6
Volume5
StatePublished - 2004
EventProceedings of the 2004 American Control Conference (AAC) - Boston, MA, United States
Duration: Jun 30 2004Jul 2 2004

Other

OtherProceedings of the 2004 American Control Conference (AAC)
CountryUnited States
CityBoston, MA
Period6/30/047/2/04

Fingerprint

Lyapunov functions
Controllers
Closed loop systems
Nonlinear systems

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Krishnamurthy, P., & Khorrami, F. (2004). Conditions for uniform solvability of parameter-dependent Lyapunov equations with applications. In Proceedings of the American Control Conference (Vol. 5, pp. 3896-3901)

Conditions for uniform solvability of parameter-dependent Lyapunov equations with applications. / Krishnamurthy, P.; Khorrami, Farshad.

Proceedings of the American Control Conference. Vol. 5 2004. p. 3896-3901.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Krishnamurthy, P & Khorrami, F 2004, Conditions for uniform solvability of parameter-dependent Lyapunov equations with applications. in Proceedings of the American Control Conference. vol. 5, pp. 3896-3901, Proceedings of the 2004 American Control Conference (AAC), Boston, MA, United States, 6/30/04.
Krishnamurthy P, Khorrami F. Conditions for uniform solvability of parameter-dependent Lyapunov equations with applications. In Proceedings of the American Control Conference. Vol. 5. 2004. p. 3896-3901
Krishnamurthy, P. ; Khorrami, Farshad. / Conditions for uniform solvability of parameter-dependent Lyapunov equations with applications. Proceedings of the American Control Conference. Vol. 5 2004. pp. 3896-3901
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