Abstract
This article investigates the memory-based state-feedback control with strict passivity performance for nonlinear systems in delta domain. Takagi–Sugeno fuzzy model of delta operator form is adopted as an approximator of the investigated nonlinear plant with system perturbations/exogenous disturbances. The nonlinear output of the plant, which is accompanied with complex exogenous disturbances, is formulated as the passive output satisfying a pre-designed strict passivity performance. The memory-based state-feedback controller is expressed with a known memory coefficient to significant the influence of the delayed states. The resulting closed-loop system is inferred as a time-varying delay system, of which the stability and passivity criterion is carried out via a general fuzzy Lyapunov–Krasovskii functional approach. Then, parametric gains of the desired strictly passive memory-based controller are designed subject to a set of solvable matrix inequalities. Finally, a numerical example shows the validity of the proposed memory-based passive control method.
Highlights
It is well known that the Takagi–Sugeno (T-S) fuzzy model[1,2] has been recognized as one of the most effective approaches to formulate complex nonlinear systems
The passive control problems have been investigated for fuzzy systems.[14,15,16]
The delta operator nonlinear plant with nonlinear controllable output is approximated by T-S fuzzy models
Summary
It is well known that the Takagi–Sugeno (T-S) fuzzy model[1,2] has been recognized as one of the most effective approaches to formulate complex nonlinear systems. In the past few decades, the problem of stability analysis and controller synthesis by the utilization of T-S fuzzy models has been widely investigated (see, for example, Feng,[3] Liu et al.,[4] Su et al.,[5] Lam and Lauber,[6] Liu et al.,[7] Wu et al.,[8] and Wei et al.[9] and references therein). A robust passive control scheme was presented in Wu et al.[16] for networked fuzzy systems with randomly occurring uncertainties
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