Abstract
This study employs a novel fuzzy co-positive Lyapunov function to investigate the stability of discrete-time polynomial-fuzzy-model-based control systems under positivity constraint. The fuzzy co-positive Lyapunov function consists of a number of local sub-Lyapunov function candidates which includes the positivity property of a non-linear system and the contribution of each sub-Lyapunov function candidates depends on the corresponding membership functions. Imperfect premise matching design concept is used for the design of a closed-loop polynomial fuzzy controller based on the constructed polynomial fuzzy model. The bounded control signal conditions (upper and lower boundary demands on control signal) are included in the Lyapunov stability and positivity conditions, in which all are formulated in the form of sum-of-squares conditions. A numerical example is given to validate the proposed approach.
Highlights
One can find examples in chemical reactors, storage systems and drug-delivery, wherein the mathematical models of the system states' response to initial positive condition is always confined in the non-negative orthant space
We increase the accuracy of system approximation by using polynomial fuzzy model to represent positive non-linear systems
This paper studies the positivity, stability and bounded control analysis of discrete-time PFMB control system based on imperfect premise matching the design concept
Summary
One can find examples in chemical reactors, storage systems and drug-delivery, wherein the mathematical models of the system states' response to initial positive condition is always confined in the non-negative orthant space. LCLF naturally hold the positivity property of a non-linear system and when using with non-negative vectors for the stability analysis of positive discrete-time PFMB control system, it shall be defined as constants to hold the positivity property of Lyapunov functions. A fuzzy co-positive Lyapunov function is employed to study stability analysis of positive discrete-time PFMB control system to relax positivity, stability and bounded control signal conditions. (ii) The fuzzy co-positive Lyapunov function is proposed for the stability of discrete-time positive PFMB control system with the non-negative vectors in the constant form This extends the formulation to more general non-negative vectors in the polynomial form which improves the generality of Lyapunov function form and reduces the conservativeness of positivity, stability and bounded control conditions.
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