Journal ArticleDOI
Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach
Yong-Yan Cao,Paul M. Frank +1 more
TLDR
The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach and a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller is presented.Abstract:
Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller.read more
Citations
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Journal ArticleDOI
A Survey on Analysis and Design of Model-Based Fuzzy Control Systems
TL;DR: A survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models.
Journal ArticleDOI
Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays
Xinping Guan,Cailian Chen +1 more
TL;DR: A guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems is introduced.
Journal ArticleDOI
On relaxed LMI-based designs for fuzzy regulators and fuzzy observers
TL;DR: A theoretical analysis shows that the proposed method provides better or at least the same results of the methods presented in the literature, and the proposed design method is applied in the control of an inverted pendulum.
Journal ArticleDOI
A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay
Jianbin Qiu,Gang Feng,Jie Yang +2 more
TL;DR: It is shown that by using a simple linearization technique incorporating a bounding inequality, a unified framework can be developed such that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software.
Journal ArticleDOI
Delay-dependent stability analysis and synthesis of uncertain T--S fuzzy systems with time-varying delay
Engang Tian,Chen Peng +1 more
TL;DR: A new method is provided by introducing some free-weighting matrices and employing the lower bound of time-varying delay and based on the Lyapunov-Krasovskii functional method, sufficient condition for the asymptotical stability of the system is obtained.
References
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Journal ArticleDOI
Fuzzy identification of systems and its applications to modeling and control
T. Takagi,Michio Sugeno +1 more
TL;DR: A mathematical tool to build a fuzzy model of a system where fuzzy implications and reasoning are used is presented and two applications of the method to industrial processes are discussed: a water cleaning process and a converter in a steel-making process.
Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Journal ArticleDOI
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Book
Theory of Functional Differential Equations
TL;DR: In this paper, Liapunov functional for autonomous systems is used to define the saddle point property near equilibrium and periodic orbits for linear systems, which is a generalization of the notion of stable D operators.
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