Robust stabilization for discrete-time Takagi-Sugeno fuzzy system based on N4SID models

Mohamed Ali Jemmali (University of Ottawa, Ottawa, Canada)
Martin J.-D. Otis (Department of Applied Sciences, University of Quebec in Chicoutimi, St Jerome, Canada)
Mahmoud Ellouze (École Nationale d’Ingénieurs de Tunis, Universite de Tunis El Manar, Tunis, Tunisia)

Engineering Computations

ISSN: 0264-4401

Publication date: 13 May 2019



Nonlinear systems identification from experimental data without any prior knowledge of the system parameters is a challenge in control and process diagnostic. It determines mathematical model parameters that are able to reproduce the dynamic behavior of a system. This paper aims to combine two fundamental research areas: MIMO state space system identification and nonlinear control system. This combination produces a technique that leads to robust stabilization of a nonlinear Takagi–Sugeno fuzzy system (T-S).


The first part of this paper describes the identification based on the Numerical algorithm for Subspace State Space System IDentification (N4SID). The second part, from the identified models of first part, explains how we use the interpolation of linear time invariants models to build a nonlinear multiple model system, T-S model. For demonstration purposes, conditions on stability and stabilization of discrete time, T-S model were discussed.


Stability analysis based on the quadratic Lyapunov function to simplify implementation was explained in this paper. The linear matrix inequalities technique obtained from the linearization of the bilinear matrix inequalities was computed. The suggested N4SID2 algorithm had the smallest error value compared to other algorithms for all estimated system matrices.


The stabilization of the closed-loop discrete time T-S system, using the improved parallel distributed compensation control law, was discussed to reconstruct the state from nonlinear Luenberger observers.



Jemmali, M., Otis, M. and Ellouze, M. (2019), "Robust stabilization for discrete-time Takagi-Sugeno fuzzy system based on N4SID models", Engineering Computations, Vol. 36 No. 4, pp. 1400-1427.

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