Title :
L2 gain analysis of piecewise linear systems using sums of squares: A negative result
Author_Institution :
Temasek Labs., Nat. Univ. of Singapore, Singapore, Singapore
Abstract :
In this paper, we investigate the L2 gain problem for piecewise linear (PWL) systems. Unlike the piecewise quadratic Lyapunov function (PQLF) approach, we construct high-order polynomial Lyapunov functions using the theory of sums of squares (SOS) with the aid of Positivstelltz and partition-dependent slack variables. We show that although more freedom is provided by SOS polynomials, the result may not be improved by linear matrix inequality (LMI) approach, i.e., SOS has its limitation in analysis of L2 gain problem for PWL systems.
Keywords :
Lyapunov methods; linear matrix inequalities; piecewise linear techniques; polynomials; L2 gain analysis; LMI approach; PWL systems; Positivstelltz variables; SOS polynomials; high-order polynomial Lyapunov function; linear matrix inequality; partition-dependent slack variables; piecewise linear systems; piecewise quadratic Lyapunov function; sums of squares; Linear systems; Lyapunov methods; Nonlinear systems; Polynomials; Silicon; Stability analysis; Vectors;
Conference_Titel :
Industrial Electronics and Applications (ICIEA), 2012 7th IEEE Conference on
Conference_Location :
Singapore
Print_ISBN :
978-1-4577-2118-2
DOI :
10.1109/ICIEA.2012.6360768
