(2017) Nguyen, Anh Tu; Sugeno, Michio; Campos, Victor Costa da Silva; Dambrine, Michel
This paper provides a computational method to
study the asymptotic stability of piecewise multi-affine systems.
Such systems stem from a class of fuzzy systems with singleton
consequents and can be used to approximate any smooth nonlinear
system with arbitrary accuracy. Based on the choice of
piecewise Lyapunov functions, stability conditions are expressed
as a feasibility test of a convex optimization with linear matrix
inequality constraints. The basic idea behind these conditions is
to exploit the parametric expressions of piecewise multi-affine
systems by means of Finsler’s lemma. Numerical examples are
given to point out the effectiveness of the proposed method.
