Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

Abstract

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016

Non‐fragile control design and state estimation for vehicle dynamics subject to input delay and actuator faults

“…Remark 2: It is noted that the inequality (12) in Definition 1 represents the condition for the extended dissipative performance which includes the H ∞ , L 2 − L ∞ , passivity, mixed H ∞ and passivity, and Q − S − R dissipativity performances as particular cases according to the selection of constant matrices Φ h , h = 1, 2, 3, 4. For any positive scalars α, γ and β, if we set Φ 1 = − I, Φ 2 = 0, Φ 3 = γ 2 I, Φ 4 = 0 and δ¯= 0, then (12) reduces to H ∞ performance; if Φ 1 = 0, Φ 2 = 0, Φ 3 = γ 2 I, Φ 4 = I and δ¯= 0, then (12) reduces to L 2 − L ∞ performance; if Φ 1 = 0, Φ 2 = I, Φ 3 = γI, Φ 4 = 0 and δ¯= 0, then (12) reduces to passivity performance; if Φ 1 = − γ −1 βI, Φ 2 = 1 − β, Φ 3 = γI, Φ 4 = 0 and δ¯= 0, then (12) reduces to mixed H ∞ and passivity performance; if Φ 1 = Q, Φ 2 = S, Φ 3 = R − αI, Φ 4 = 0 and δ¯= 0, then (12) reduces to Q − S − R dissipativite performance.…”

“…Since the realistic non-linear models are too complex, there is no general structure for their control and identification. Nevertheless, the Takagi-Sugeno (T-S) fuzzy model has widely been employed to represent the non-linear systems in which the non-linear systems are approximated by a convex combination of linear models [11][12][13][14]. Based on the T-S fuzzy model approach, several vehicle dynamics problems have been solved in the literature (see, for instance [15,16]).…”

Design of a Fault Tolerant Sampled-Data Fuzzy Observer With Exponential Time-Varying Gains

“…Remark 2: In the observer model, F(t k ) represents the sensor failure. F(t k ) is generally a time-varying unknown matrix, but, following the study [30], this paper assumes that both the upper and lower bounds of its norm are known.…”

“…To guarantee the H ∞ performance criterion (6), adding e 2αt ε T (t)ε(t) − γ 2 W T (t)W (t) toV (t) and summarizing (27), (29), (30), and (37) yielḋ…”

“…Similar to the sensor fault, actuator fault is also the serious problem in the control engineering. In [30], fault tolerant control was studied by assuming the actuator fault as a time-varying uncertainty in the gain matrix. This method is simple and powerful to handle the actuator fault.…”