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This paper presents a practical discrete-time fractional order terminal sliding mode (DFOTSM) control strategy for high-precision tracking tasks based on a linear motor. In particular, the practical parametric uncertainties involving sliding friction, uncertain payload, and disturbance in tracking tasks are considered in this paper. Combining Grünwald–Letnikov fractional order definition and terminal sliding mode technique, the proposed method synthesizes a novel DFOTSM control law to drive the sliding mode dynamics into the stable region in finite steps theoretically, even though the system is suffering from uncertainties and disturbances, and the motion on the surface can guarantee higher tracking precision than the conventional discrete-time terminal sliding surface by selecting suitable controller parameters. The theoretical analyses give out the guideline of parameter selection, and experiments are carried out on the linear-motor-based test platform to demonstrate that the proposed controller is easily implemented and can achieve high-precision tracking, fast response, and considerable robustness to uncertainties. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the stability and stabilization problem of a class of discrete‐time switched systems with mode‐dependent average dwell time (MDADT). A novel Lyapunov function, which is both mode‐dependent (MD) and quasi‐time‐dependent (QTD), is established. The new established Lyapunov function is allowed to increase at some certain time instants. A QTD H ∞ controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed H ∞ performance index. The new QTD robust controller designed in this paper is less conservative than the mode independent one which is frequently considered in literatures. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the developed results. H ∞ [ABSTRACT FROM AUTHOR]

This study investigates the fuzzy control problem for a class of non‐linear Markov jump systems with sampled‐data inputs and actuator constraints over a finite‐time interval. Takagi–Sugeno (T–S) fuzzy models are employed to approximate the non‐linearity. The partly known transition probability matrix consisting of known, uncertain, and unknown elements is considered. The asynchronous errors of the membership functions induced by aperiodic sampling are taken care of to avoid conservative results. The objective is to procure a sampled‐data fuzzy controller such that the resulting closed‐loop system is finite‐time bounded and a prescribed performance index is guaranteed simultaneously. By establishing a new piecewise Lyapunov–Krasovskii functional and utilising convex optimisation technique, a novel set of sufficient conditions for the existence of anticipated sampled‐data controller are developed. Finally, two illustrative examples are presented to prove the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust dissipative control is investigated for uncertain flexible spacecraft based on Takagi–Sugeno (T–S) fuzzy model with saturated time-delay input. Different from most existing strategies, T–S fuzzy approximation approach is used to model the nonlinear dynamics of flexible spacecraft. Simultaneously, the physical constraints of system, like input delay, input saturation, and parameter uncertainties, are also taken care of in the fuzzy model. By employing Lyapunov–Krasovskii method and convex optimization technique, a novel robust controller is proposed to implement rest-to-rest attitude maneuver for flexible spacecraft, and the guaranteed dissipative performance enables the uncertain closed-loop system to reject the influence of elastic vibrations and external disturbances. Finally, an illustrative design example integrated with simulation results are provided to confirm the applicability and merits of the developed control strategy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of robust adaptive stabilization of uncertain stochastic jumping dynamical networks with mode-dependent mixed delays is investigated. The mixed delays are composed of time-varying delays and distributed delays, both of which are mode dependent. By adaptive feedback technique, several sufficient criteria are derived to ensure the global asymptotical stability in mean square for the uncertain stochastic dynamical networks with mixed delays and Markovian jumping parameters. The controller is easy to implement in practical situations. In the end, the corresponding simulation results are constructed to support the theoretical results in this paper. [Copyright &y& Elsevier]