Griggs, Wynita M. and King, Christopher K. and Shorten, Robert N. and Mason, Oliver and Wulff, Kai
Quadratic Lyapunov Functions for Systems with
Linear Algebra and its Applications, 333 (1).
In this paper, we consider the existence of quadratic Lyapunov functions for certain
types of switched linear systems. Given a partition of the state-space, a set of matrices
(linear dynamics), and a matrix-valued function A(x) constructed by associating these
matrices with regions of the state-space in a manner governed by the partition, we ask
whether there exists a positive definite symmetric matrix P such that A(x)T P +PA(x)
is negative definite for all x(t). For planar systems, necessary and sufficient conditions
are given. Extensions for higher order systems are also presented.
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