Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems

A New Stochastic Sliding-Mode Design for Descriptor Fuzzy Systems With Time-Varying Delay

In this article, by use of sliding-mode control, a descriptor stochastic fuzzy system with time-varying delay is considered. First, a new sliding-mode surface is proposed. By use of it, the fuzzy system with different input matrices could be studied. At the same time, the controlled system still has strong robustness to external disturbance. Second, since time delay is variable, there is not the time-delay term in the function of the new sliding-mode surface. It makes the controller construct hard. Third, the process of constructing the controller is different from the traditional method. The process of designing the controller does not use the border of external disturbance. Using a new self-adaptive method, the considered system reaches and is kept on the surface. Unlike the earlier sliding-mode controller, the virtue of this controller is that the fluctuation of the controller is small. Finally, two simulations are given to illustrate the effect of this method.

Observer-Based Non-PDC Control for Networked T-S Fuzzy Systems With an Event-Triggered Communication

This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi-Sugeno (T-S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions. First, a unified event-triggered T-S fuzzy model is provided, in which: 1) a fuzzy observer with the imperfect premise matching is constructed to estimate the unmeasurable states of the studied system; 2) a fuzzy controller is designed following the same premise as the observer; and 3) an output-based event-triggering transmission scheme is designed to economize the restricted network resources. Different from the traditional PDC method, the synchronous premise between the fuzzy observer and the T-S fuzzy system are no longer needed in this paper. Second, by use of Lyapunov theory, a stability criterion and a stabilization condition are obtained for ensuring asymptotically stable of the studied system. On account of the imperfect premise matching conditions are well considered in the derivation of the above criteria, less conservation can be expected to enhance the design flexibility. Compared with some existing emulation-based methods, the controller gains are no longer required to be known a priori. Finally, the availability of proposed non-PDC design scheme is illustrated by the backing-up control of a truck-trailer system.

Relaxed observer design of discrete-time T-S fuzzy systems via a novel slack variable approach

The problem of further studies on observer design for discrete-time Takagi-Sugeno fuzzy systems is investigated in this paper. Different from the existing result, a new slack variable approach is presented by developing some useful matrix equalities which rely on both the current-time and the past-time normalized fuzzy weighting functions. As a result, the relaxation quality of recent fuzzy observer design is significantly enhanced. Moreover, the conditions for the existence of a fuzzy H(∞) observer that minimizes an upper bound to H(∞) norms are also proposed. Finally, two numerical examples are provided to show that the given results are less conservative than other results available in the literature.

Robust Design of Fuzzy Structured Controllers via a Moving Boundaries Process

In this paper, we consider the design of a fuzzy structured controller for systems that can be well described by uncertain T-S fuzzy models. Finding such a controller is known to be computationally intractable by the conventional techniques. Therefore, to solve this design problem easily and directly, we utilize a moving boundary process together with a robust stability test, for finding a solution to the corresponding feasibility problem. Some design examples are presented to illustrate the main points introduced in this paper.

Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach

This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.