Robust H/sub /spl infin// control for fuzzy systems with Frobenius norm-bounded uncertainties

2006 ◽  
Vol 14 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Ji-Chang Lo ◽  
M.-L. Lin
Keyword(s):  
Fuzzy Systems ◽  
Frobenius Norm ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

Robust Control for Uncertain Takagi–Sugeno Fuzzy Systems with Time-Varying Input Delay

2004 ◽  
Vol 127 (2) ◽  
pp. 302-306 ◽  
Author(s):  
Ho Jae Lee ◽  
Jin Bae Park ◽  
Young Hoon Joo
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Input Delay ◽  
Time Varying ◽  
Convex Optimization Problem ◽  
Variation Rate ◽  
Mass Spring ◽  
Takagi Sugeno ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

A control problem of Takagi–Sugeno fuzzy systems with a time-varying input delay and norm-bounded uncertainties is addressed. The input delay is well-known in making the closed-loop stabilization difficult. A sufficient condition for the robust fuzzy-model-based stabilization is derived based on the Lyapunov–Razumikhin stability theorem, without the assumption of the variation rate on the delay. A constructive design scheme is presented in the form of the iterative convex optimization problem. The effectiveness of the proposed method is demonstrated by a numerical simulation of a nonlinear mass-spring-damper system.

scholarly journals Robustl2−l∞Filtering for Takagi-Sugeno Fuzzy Systems with Norm-Bounded Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Wenbai Li ◽  
Yu Xu ◽  
Huaizhong Li
Keyword(s):  
Fuzzy Systems ◽  
Filter Design ◽  
Weighting Function ◽  
Original System ◽  
Peak Performance ◽  
System 2 ◽  
Error System ◽  
Takagi Sugeno ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

We study the filter design problem for Takagi-Sugeno fuzzy systems which are subject to norm-bounded uncertainties in each subsystem. As we know that the Takagi-Sugeno fuzzy linear systems can be used to represent smooth nonlinear systems, the studied plants can also be uncertain complex systems. We suppose to design a filter with the order of the original system which is also dependent on the normalized fuzzy-weighting function; that is, the filter is also a Takagi-Sugeno fuzzy filter. With the augmentation technique, an uncertain filtering error system can be obtained and the system matrices in the filtering error system are reorganized into two categories (without uncertainties and with uncertainties). For the filtering error system, we have two objectives. (1) The first one is that the filtering error system should be robust stable; that is, the filtering error system is stable though there are uncertainties in the original system. (2) The second one is that the robust energy-to-peak performance should be guaranteed. With the well-known Finsler’s lemma, we provide the conditions for the robust energy-to-peak performance of the filtering error system in which three slack matrices are introduced. Finally, a numerical example is used to show the effectiveness of the proposed design methodology.

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

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