Output stabilization of Takagi-Sugeno fuzzy systems.

*(English)*Zbl 0991.93069The authors discuss a class of Takagi-Sugeno models governed by rules of the form
\[
\text{-if } z_1\text{ is }M_{1i} \text{ and\dots and }z_p \text{ is }M_{pi} \text{ then }dx/dt= A_ix(t)+B_i u(t),\;y(t)=C_ix(t)
\]
(in the above \(x(t)\in \mathbb{R}^n\), \(u(t)\in \mathbb{R}^m\) and \(y(t)\in \mathbb{R}^q\), \(i=1, 2, \dots,r\); \(M_{1i},\dots,M_{pi}\) are fuzzy sets contained in the condition part of the rule).

The problem under consideration deals with output stabilization in this class of models. Starting from observers formed for each rule (subsystem), sufficient conditions are provided for their asymptotic convergence. It is shown that a state feedback controller and an observer yield a stabilizing output feedback controller (assuming that the stabilizing property of the control and an asymptotic convergence of the observer are guaranteed by the Lyapunov method).

The problem under consideration deals with output stabilization in this class of models. Starting from observers formed for each rule (subsystem), sufficient conditions are provided for their asymptotic convergence. It is shown that a state feedback controller and an observer yield a stabilizing output feedback controller (assuming that the stabilizing property of the control and an asymptotic convergence of the observer are guaranteed by the Lyapunov method).

Reviewer: Witold Pedrycz (Edmonton)

##### MSC:

93C42 | Fuzzy control/observation systems |

93D15 | Stabilization of systems by feedback |

93B07 | Observability |

##### Keywords:

fuzzy control; separation principle; Takagi-Sugeno models; output stabilization; observers; asymptotic convergence; Lyapunov method
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\textit{J. Yoneyama} et al., Fuzzy Sets Syst. 111, No. 2, 253--266 (2000; Zbl 0991.93069)

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