Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 27, Issue 11, Pages 2090-2100Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2019.2893344
Keywords
Delay effects; Stability analysis; Mathematical model; Analytical models; Control systems; Lyapunov methods; Discrete-time systems; Discrete-time polynomial fuzzy-model-based (PFMB) control systems with time delay; positive systems; piecewise linear membership functions (PLMFs); premise variables; stability analysis; SOS
Funding
- Queen Mary University of London
- Chinese Scholarship Council
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This paper proposes a novel Lyapunov stabilization analysis of discrete-time polynomial-fuzzy-model-based control systems with time delay under positivity constraint. The polynomial fuzzy model is constructed to describe the dynamics of a nonlinear discrete-time system with time delay. A model-based polynomial fuzzy controller is designed using nonparallel distributed compensation technique to stabilize the system while driving the system states to positive using the positivity constraints. The Lyapunov stability and positivity conditions are formulated as sum-of squares. To relax the conservativeness of the obtained stability results, two main methods are proposed in this paper: first, the piecewise linear membership functions (PLMFs) are used to introduce the approximate error between piecewise and the original membership functions into the stability analysis; and second, introduce the boundary information of the premise variables into the stability analysis since the premise variables hold rich nonlinearity information. A numerical example is given to demonstrate the effectiveness of the proposed approach.
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