access icon openaccess Stability analysis of discrete-time positive polynomial-fuzzy-model-based control systems through fuzzy co-positive Lyapunov function with bounded control

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.

Inspec keywords: polynomials; nonlinear control systems; Lyapunov methods; closed loop systems; linear systems; fuzzy set theory; discrete time systems; stability; fuzzy control; control system synthesis; position control

Other keywords: control signal conditions; co-positive Lyapunov function; positivity property; local sub-Lyapunov function candidates; closed-loop polynomial fuzzy controller; Lyapunov stability; positivity constraint; discrete-time positive polynomial-fuzzy-model-based control systems; discrete-time polynomial-fuzzy-model-based control systems; bounded control; corresponding membership functions; constructed polynomial fuzzy model; positivity conditions

Subjects: Spatial variables control; Interpolation and function approximation (numerical analysis); Algebra; Stability in control theory; Control system analysis and synthesis methods; Linear control systems; Discrete control systems; Nonlinear control systems; Combinatorial mathematics; Fuzzy control

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