Convergent robust stabilization conditions for fuzzy chaotic systems based on the edgewise subdivision approach

This paper concerns the problem of stabilizing fuzzy chaotic systems via the viewpoint of the edgewise subdivision approach. Firstly, a new edgewise subdivision algorithm is proposed to implement the simplex edgewise subdivision which divides the overall fuzzy chaotic systems into a lot of sub-systems by a kind of algebraic description. These sub-systems have the same volume and shape characteristics. Secondly, a novel kind of control scheme which switches by the transfer of different operating sub-systems is proposed to achieve convergent stabilization conditions for the underlying controlled fuzzy chaotic systems. Finally, a numerical example is given to demonstrate the validity of the proposed methods.

A new neural network model for the feedback stabilization of nonlinear systems

A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constraints are shown to be a set of linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law. Most recurrent neural networks (including the chaotic neural network) and nonlinear systems modeled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM. Finally, three numerical examples are provided to illustrate the design developed in this paper.

Decay rate performance approach for stabilization continuous fuzzy models using their discretized forms

Purpose–The purpose of this paper is to deal with the stabilization of the continuous Takagi Sugeno(TS)fuzzy models using their discretized forms based on the decay rate performance approach.Design/methodology/approach–This approach is structured as follows:first,a discrete model is obtained from the discretization of the continuous TS fuzzy model.The discretized model is obtained from the Euler approximation method which is used for several orders.Second,based on the decay rate stabilization conditions,the gains of a non-PDC control law ensuring the stabilization of the discrete model are determined.Third by keeping the values of the gains,the authors determine the values of the performance criterion and the authors check by simulation the stability of the continuous TS fuzzy models through the zero order hold.Findings–The proposed idea lead to compare the performance continuous stability results with the literature.The comparison is,also,taken between the quadratic and non-quadratic cases.Originality/value–Therefore,the originality of this paper consists in the improvement of the continuous fuzzy models by using their discretized models.In this case,the effect of the discretization step on the performances of the continuous TS fuzzy models is studied.The usefulness of this approach is shown through two examples.

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model （SNNM）, is advanced to describe some delayed （or non-delayed） discrete-time intelligent systems composed of neural networks and Takagi and Sugeno （T-S） fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities （LMIs） which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based （or fuzzy） discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based （or fuzzy） discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.