Quadratic Lyapunov Functions for Systems with State-Dependent Switching
Griggs, Wynita M. and King, Christopher K. and Shorten, Robert N. and Mason, Oliver and Wulff, Kai (2010) Quadratic Lyapunov Functions for Systems with State-Dependent Switching. Linear Algebra and its Applications, 333 (1). pp. 52-63. ISSN 0024-3795
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.
Repository Staff Only: item control page