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Stability and Constrained Control of a Class of Discrete-Time Fuzzy Positive Systems with Time-Varying Delays
Authors:Yanbing Mao  Hongbin Zhang  Yan Qin  Chuangyin Dang
Affiliation:1. Centre for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China
2. School of Statistics, Southwestern University of Finance & Economics, Chengdu, 610074, P.R. China
3. Department of Systems Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong
Abstract:
This paper deals with the stability of nonlinear discrete-time positive systems with time-varying delays represented by the Takagi–Sugeno (T–S) fuzzy model. The time-varying delays in the systems can be unbounded. Sufficient conditions of stability which are not relevant to the magnitude of delays are derived by a solution trajectory. Based on the stability results, the problems of controller design via the parallel distributed compensation (PDC) scheme are solved. The control is under the positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained control is also considered, further requiring that the state trajectory of the closed-loop system be bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results and control laws are formulated as linear matrix inequalities (LMIs) and linear programs (LPs). A numerical example and a real plant are studied to demonstrate the application of the proposed methods.
Keywords:
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