Abstract
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.
Highlights
A SPECIAL class of physical systems in the real world involve quantities that have an intrinsically constant sign, such as absolute temperatures, the concentration of substances in the chemical process, level of liquids in tanks, and so on [1]–[5]
This paper proposed a novel Lyapunov approach to reduce the conservativeness of positivity and stability conditions, which are used for the stability analysis and controller design of discretetime polynomial fuzzy-model-based (PFMB) control systems with time delay
To automate the whole analysis as a feasibility problem, all the Lyapunov stability conditions and the non-parallel distributed compensation (PDC) design of controller gains are formulated as SOS conditions
Summary
A SPECIAL class of physical systems in the real world involve quantities that have an intrinsically constant sign, such as absolute temperatures, the concentration of substances in the chemical process, level of liquids in tanks, and so on [1]–[5]. To relax the stability conditions for positive continuous fuzzy-model-based control systems with time delay, a few attempts have been made to introduce the information of membership functions in the stability analysis [29], [30]. 2) Non-PDC design concept is used to design the controller for polynomial fuzzy model-based systems with time delay, and investigate the stability and positivity analysis, leading to an increase to the design flexibility by choosing the number of rules and shape of membership functions of the fuzzy controller freely.
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