Control Synthesis of Discrete-Time T–S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach

Abstract

This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.

Distributed non-fragile filtering for T-S fuzzy systems with event-based communications

“…A simulation study on the robotic system has been presented to show the effectiveness of the proposed new design. The future attention would be paid onto the conservatism reduction of the filter design and the results in [33] may be helpful to achieve this goal. On the other hand, the distributed filtering for a more general fuzzy systems, such as Interval Type-2 Takagi-Sugeno Fuzzy Systems [34,35] is also an interesting topic that needs to be invesitgated in future.…”

Adaptive fuzzy backstepping output constraint control of flexible manipulator with actuator saturation

“…In [43,44], the authors have applied the optimal control theory and saturation arithmetic to the control methods, and the considered systems also contain timevarying delay; therefore, the methods they have proposed in [43,44] cannot be used in this paper. In the future study, we will be concentrated on the adaptive fuzzy output feedback control design for uncertain nonlinear systems with time-varying delay based on the results of this paper and references [43][44][45][46].…”

Reduced-order model approximation of fuzzy switched systems with pre-specified performance

“…Since the nonlinear system can be modelled as a weighted total of combined linear sub-models via T-S fuzzy modelling, researchers have put a great deal of efforts into T-S fuzzy systems and numerous achievements have been obtained in this research field. To mention a few, the receding horizon disturbance attenuation analysis and dynamic decoupling are studied in [2,7], the fuzzy controllers are designed for nonlinear systems in [16,32,34,42], the the fault detection and H ∞ synchronization problem are solved in [17,30], the fuzzy-rule-dependent stability analysis and control problems are studied in [11,12,13,18], and the fuzzy filtering problems with the given pre-specified performance are investigated in [1,44].…”