Abstract
The paper presents new conditions suitable in design of a stabilizing output controller for a class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the fuzzy control scheme relating to the parallel distributed output compensators, the sufficient design conditions are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and guarantees global stability of the system. Simulation result illustrates the design procedure and demonstrates the performances of the proposed design method.
Highlights
To the linear framework, nonlinear systems are too complex to be represented by uni ed mathematical resources, and so a generic method has not been developed yet to design a controller valid for all types of nonlinear systems
E main contribution of the paper is the presentation of the original design condition of the fuzzy output feedback control for the continuous-time nonlinear multiinput and multioutput nonlinear (MIMO) systems approximated by a TS model. e central idea of the TS fuzzy model-based control design, that is, to derive control rules so as to compensate each rule of a fuzzy system and construct the control strategy based on the parallel distributed compensators, is re ected in the approach of output control, taking into account the fact that the desired output variables are measurable
The fuzzy output controller is designed using the concept of parallel distributed compensation, in which the fuzzy controller shares the same sets of normalized membership functions like the TS fuzzy system model
Summary
To the linear framework, nonlinear systems are too complex to be represented by uni ed mathematical resources, and so a generic method has not been developed yet to design a controller valid for all types of nonlinear systems. A range of stability analysis conditions [2,3,4,5], as well as control design methods [6,7,8,9,10,11], have been developed for TS fuzzy systems, relying mostly on the feasibility of an associated set of linear matrix inequalities (LMI) [12]. E main contribution of the paper is the presentation of the original design condition of the fuzzy output feedback control for the continuous-time nonlinear MIMO systems approximated by a TS model. Each triplet (AAii, BBii, CC) is locally controllable and observable, the matrix CC is the same for all local models, and the number of input variables is equal to the number of output variables It is supposed in the following considerations that the aforementioned model does not include parameter uncertainties or external disturbances, and the premise variables are measured
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