Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems

Filtering for Switched T-S Fuzzy Systems With Persistent Dwell Time

The H_∞ filter design for a class of switched Takagi-Sugeno (T-S) fuzzy systems with persistent dwell time (PDT) is investigated in this paper. The considered switched fuzzy systems contain a limited number of subsystems and each local subsystem is represented by the well-known T-S fuzzy model. Compared with the dwell time (DT) switching or average DT switching that attracted quantities of interests over the last decade, the PDT switching considered in this paper is known to be more general. The stability and L ₂ -gain analysis for switched systems with PDT switching are derived first, based on which a set of full-order H_∞ filter is designed to guarantee the global uniform asymptotic stability with a prescribed nonweighted H_∞ noise attenuation performance for the resulting filtering error system. Finally, the effectiveness of the provided method is illustrated with an example.

A Simple, Natural and Effective Framework of Nonlinear Systems Control and its Application to Aerial Robots

This paper presents a simple, natural and effective framework of nonlinear systems control and its application to aerial robots. First, we present a framework of Takagi-Sugeno fuzzy model-based control and also discuss its feature. Next, a number of design problems for the control framework are formulated as numerically feasibility problems of representing in terms of linear matrix inequalities. Finally, we provide two applications of the control framework to aerial robots. The control results of aerial robots show the utility of the control framework.

T-S-Fuzzy-Model-Based Approximation and Controller Design for General Nonlinear Systems

This paper presents a novel approach to control general nonlinear systems based on Takagi-Sugeno (T-S) fuzzy dynamic models. It is first shown that a general nonlinear system can be approximated by a generalized T-S fuzzy model to any degree of accuracy on any compact set. It is then shown that the stabilization problem of the general nonlinear system can be solved as a robust stabilization problem of the developed T-S fuzzy system with the approximation errors as the uncertainty term. Based on a piecewise quadratic Lyapunov function, the robust semiglobal stabilization and H∞ control of the general nonlinear system are formulated in the form of linear matrix inequalities. Simulation results are provided to illustrate the effectiveness of the proposed approaches.

Switching Fuzzy Model Construction and Controller Design for Dynamical Systems with Input Nonlinearity

Fuzzy model-based control mainly deals with dynamical systems which affinely depend on control inputs. In this paper, dynamical systems which is permitted to have nonlinearity not only in the states, but also in the inputs is considered. Input nonlinearity makes a nonlinear system complicated and makes the number of fuzzy model rules increase. Thus, switching fuzzy control approach is employed. Firstly, the switching fuzzy model construction with arbitrary linear dividing planes, which is an extension of the ordinary switching fuzzy model construction method with dividing planes corresponding to quadrants, is introduced. Secondly, by applying the switching fuzzy model construction method to the dynamical system with input nonlinearity, the switching fuzzy model with membership functions which depend on control inputs is constructed. Finally, by utilizing the dynamic state feedback control approach, we show that membership functions which depend on control inputs can be calculated. Moreover, by employing augmented system approach, the switching fuzzy dynamic state feedback controller design conditions based on the switching Lyapunov function are derived in terms of linear matrix inequalities. A design example illustrates the utility of this approach.