Abstract
This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a state-feedback passive controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. The existence conditions of the controller can be expressed by linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the feasibility and effectiveness of the proposed method.
Highlights
It is well known that the fuzzy logic control [1,2,3,4] is one of the most effective approaches to handle complex nonlinear systems
This section focuses on designing a sufficient condition for the solvability of the proposed passive control problem and a developed linear matrix inequalities (LMIs) approach for designing the passive controller for fuzzy system (5)
Considering fuzzy delta operator system (5), for a given sampling period T > 0, constants dm, dM (0 < dm ≤ dM), and matrix Ks (s = 1, 2, . . . , r), system (5) is very strictly passive if there exist scalars ε > 0, ζ > 0 and symmetric matrices P > 0, R1 > 0, R2 > 0, Qκ > 0, S1κ > 0, and S2κ > 0 (κ = 1, 2, . . . , r) with appropriate dimensions, such that the following LMIs hold for κ, λ, μ, ], i, s = 1, 2, . . . , r: Θκλμ]ii < 0, (20)
Summary
It is well known that the fuzzy logic control [1,2,3,4] is one of the most effective approaches to handle complex nonlinear systems. Takagi-Sugeno (T-S) fuzzy model has been proposed in [5] and applied to formulate a complex nonlinear systems into a framework. By T-S fuzzy model, a set of complex nonlinear systems can be possibly described as a weighed sum of some simple linear subsystems. The problem of stability analysis and controller synthesis of nonlinear systems in T-S fuzzy model has been extensively investigated in [5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Due to the effect of time delay in systems, the problems of T-S fuzzy systems with time delays have got considerable attention in recent years, and some results have been developed in [9, 19,20,21,22,23,24,25,26,27,28,29,30,31]
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