Paper Info
Title
A Kalman-Yakubovich-Popov-type lemma for systems with certain state-dependent constraints
Abstract
In this note, a result is presented that may be considered an extension of the classical Kalman–Yakubovich–Popov (KYP) lemma. Motivated by problems in the design of switched systems, we wish to infer the existence of a quadratic Lyapunov function (QLF) for a nonlinear system in the case where a matrix defining one system is a rank-1 perturbation of the other and where switching between the systems is orchestrated according to a conic partitioning of the state space R n . We show that a necessary and sufficient condition for the existence of a QLF reduces to checking a single constraint on a sum of transfer functions irrespective of problem dimension. Furthermore, we demonstrate that our conditions reduce to the classical KYP lemma when the conic partition of the state space is R n , with the transfer function condition reducing to the condition of Strict Positive Realness.
Year
DOI
Venue
2011
10.1016/j.automatica.2011.06.016
Automatica
Keywords
Field
DocType
kalman-yakubovich-popov lemma,sufficient condition,linear matrix inequality,quadratic lyapunov function,frequency domain inequality,conic partition,state space r,kalman-yakubovich-popov-type lemma,lyapunov function,state space,transfer function condition,nonlinear system,classical kyp lemma,conic partitioning,certain state-dependent constraint,nonlinear systems,switched systems,convex cone,state-dependent constraints,classical kalman-yakubovich-popov,transfer function,frequency domain
Lyapunov function,Mathematical optimization,Nonlinear system,Control theory,Kalman–Yakubovich–Popov lemma,Transfer function,Conic section,State space,Lemma (mathematics),Mathematics,Convex cone
Journal
Volume
Issue
ISSN
47
9
Automatica
Citations 
PageRank 
References 
3
0.39
5
Authors
3
Name
Order
Citations
PageRank
Christopher K. King1264.50
Wynita M. Griggs28113.39
Robert N. Shorten31378.51