access icon free Membership-dependent stability analysis of discrete-time positive polynomial fuzzy-model-based control systems with time delay

© The Institution of Engineering and Technology
Received 25/06/2019, Accepted 02/01/2020, Revised 20/11/2019, Published 02/03/2020

This study proposes a novel, relaxed, Lyapunov-based and membership-function dependent stabilisation analysis of discrete-time polynomial-fuzzy-model-based (PFMB) control systems with time delay under positivity constraint. The discrete-time non-linear system with time delay is represented by a polynomial fuzzy model, and corresponding PFMB controller is designed using imperfect premise matching technique which does not require its fuzzy rule and shape of membership functions be matched with those of the model. The authors take advantage of this property to relax the conservativeness of the obtained stability results by introducing the information of membership functions, i.e. the relationship constraint information of membership functions between the model and the controller and boundary information of membership functions, into the stability and positivity conditions. A numerical example is given to demonstrate the effectiveness of the proposed approach.

Inspec keywords: fuzzy control; linear matrix inequalities; fuzzy set theory; linear systems; nonlinear control systems; control system synthesis; discrete time systems; control system analysis; stability; polynomials; Lyapunov methods; delays

Other keywords: polynomial fuzzy model; positivity conditions; membership-function dependent stabilisation analysis; discrete-time nonlinear system; discrete-time positive polynomial fuzzy-model-based control systems; boundary information; membership functions; Lyapunov-based; corresponding PFMB controller; positivity constraint; membership-dependent stability analysis; discrete-time polynomial-fuzzy-model-based control systems; time delay; imperfect premise matching technique; fuzzy rule

Subjects: Nonlinear control systems; Algebra; Discrete control systems; Stability in control theory; Combinatorial mathematics; Fuzzy control; Linear control systems; Control system analysis and synthesis methods

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