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Article Dans Une Revue Annual Reviews in Control Année : 2009

Discrete Tagaki-Sugeno models for control: Where are we?

Résumé

This work deals with relaxed conditions for stability and stabilization of discrete-time Takagi–Sugeno (TS) models. It recalls classical results found in the literature which use quadratic Lyapunov functions leading to very conservative conditions, and various extensions based on piecewise and non-quadratic Lyapunov functions. Afterwards, a new and powerful way to enhance the previous results is depicted. The basic idea is that waiting long enough a stable model will converge towards its equilibrium and, therefore, the Lyapunov functions under consideration are not necessarily decreasing at every sample, but are allowed to decrease every k samples. Whatever it is k >1, the results are proved to include the standard one-sample case. The potential of this approach is shown through several examples in the paper.

Dates et versions

hal-00519406 , version 1 (20-09-2010)

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Thierry-Marie Guerra, Alexandre Kruszewski, Jimmy Lauber. Discrete Tagaki-Sugeno models for control: Where are we?. Annual Reviews in Control, 2009, 33 (1), pp.37-47. ⟨10.1016/j.arcontrol.2009.01.004⟩. ⟨hal-00519406⟩
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