Open AccessNew Stability Conditions for Nonlinear Systems Described by Multiple Model Approach
Author(s) -
Ameur Sassi,
Afef Abdelkrim
Publication year - 2016
Publication title -
international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.277
H-Index - 22
ISSN - 2088-8708
DOI - 10.11591/ijece.v6i1.pp177-187
Subject(s) - control theory (sociology) , nonlinear system , stability (learning theory) , basis (linear algebra) , computer science , exponential stability , tracking (education) , linear matrix inequality , lyapunov stability , lyapunov function , matrix (chemical analysis) , mathematics , control (management) , mathematical optimization , artificial intelligence , psychology , pedagogy , physics , geometry , materials science , quantum mechanics , machine learning , composite material
This paper studies the global asymptotic stability and the tracking control problem of an uncertain non stationary continuous system described by the multiple model approach. It is based on the construction of a basis of models containing four extreme models and possibility of addition of an average model. Once the basis of models is generated, an operation of fusion of these different models is made to the level of the elementary control law and the partial output using the geometric method. New sufficient conditions for the stability are derived via Lyapunov technique. The matrices of feedback gains and tracking gains are determined while solving systems of LMI constraints (Linear Matrix Inequalities). The case of an unstable continuous nonlinear model of electrical circuit operating in pseudo-periodic system is considered to illustrate the proposed approach.