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Zbl 0992.93084
Shorten, Robert; Ó Cairbre, Fiacre
A proof of global attractivity for a class of switching systems using a non-quadratic Lyapunov approach.
(English)
[J] IMA J. Math. Control Inf. 18, No.3, 341-353 (2001). ISSN 0265-0754; ISSN 1471-6887/e

The authors consider the switched system $$\dot x+A(t)x$$ where $A(t)$ is piecewise constant and takes a finite number of values $A_i$, $i=1,\dots,m$. The exponential stability of this system is ensured by the existence of a common quadratic Lyapunov function $x^TPx$ for all constituent system $$\dot x=A_ix,\ i=i,\dots,m.$$ Some new conditions for the existence of such a function are considered; the known conditions are weakened in the sense that upper triangularization of the $A_i$ no longer needs to be performed via a common similarity transformation.
MSC 2000:
*93D30 Scalar and vector Lyapunov functions
93B12 Variable structure systems
93D20 Asymptotic stability of control systems

Keywords: asymptotic stability; switched system; exponential stability; common quadratic Lyapunov function

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