Stability and performances synthesis of a class of Takagi–Sugeno systems with unmeasured premises: restricted-model-based approach

Sonia Maalej and Alexandre Kruszewski

International Journal of Systems Science, 2023, vol. 54, issue 2, 443-461

Abstract: This paper presents the design of a robust Restricted-Model-Based control providing tools for both stability and performance analysis of a class of Single-Input-Single-Output (SISO) Takagi–Sugeno (T–S) systems. The proposed method is evaluated in terms of induced $ \mathcal {L}_2 $ L2-gain (or so-called $ \mathcal {H}_{\infty } $ H∞ norm) to be robust to disturbances, sensor noises and uncertainties on the premise variables. Unlike the common approaches reported in the literature that consider exact premise variables, this work deals with the problem of unmeasured premises. The main results of this paper illustrate that stability and performance conditions can be evaluated by examining the feasibility of parametrised sets of linear matrix inequalities (LMIs). The proof of stability is based on the non-linear sector approach of the closed loop under Lyapunov conditions, $ \mathcal {L}_2 $ L2 norm and system transformations. The result is a control structure with only one parameter tuned via simple conditions. The performance and applicability of the proposed approach are illustrated through numerical simulations of an academic example.

Date: 2023
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DOI: 10.1080/00207721.2022.2122900

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