Title :
On quadratic Lyapunov functions
Author :
Cheng, Daizhan ; Guo, Lei ; Huang, Jie
Author_Institution :
Inst. of Syst. Sci., Chinese Acad. of Sci., Beijing, China
fDate :
5/1/2003 12:00:00 AM
Abstract :
A topological structure, as a subset of [0,2π)L×R+n-1, is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral. The structure and the conditions are considerably simplified for planar systems. It is also proved that a set of block upper triangular matrices share a common QLF, if each set of diagonal blocks share a common QLF.
Keywords :
Lyapunov methods; linear systems; matrix algebra; stability; topology; matrix algebra; necessary condition; quadratic Lyapunov functions; stabilization; stable linear system; sufficient condition; switched system; topological space; topological structure; Automatic control; Lyapunov method; MIMO; Nonlinear control systems; Nonlinear equations; Nonlinear systems; Regulators; Servomechanisms; Switched systems; Transmission line matrix methods;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2003.811274
