In this work, a novel discrete-time fractional-order sliding mode control (SMC) scheme is proposed, which guarantees the desired tracking performance of a linear motor control system. By using Euler’s discretization method, a discrete-time model is firstly established for the linear motor, which includes the nonlinear friction and the uncertainties. Considering the practicability of the engineering application, a new discrete-time fractional-order sliding surface is constructed by taking the Grünwald–Letnikov definition based fractional-order difference of the tracking error into account. Compared to the classical integer-order sliding surface, by the proposed fractional-order sliding surface in this work, a better performance can be achieved due to the memory effect of the fractional calculus. To drive the system trajectories to the predefined sliding surface in finite sampling steps, a novel equivalent control is then designed, which can adjust the switching control input adaptively. Meanwhile, the theoretical analysis for the tracking error of the linear motor system is presented, and the practical reachability of the sliding surface is validated by numerical simulations. Finally, the effectiveness of the proposed control strategy is verified by a group of tracking experiments on a linear motor platform.

This paper is concerned with event-triggered sliding mode control (SMC) for uncertain stochastic systems subject to limited communication capacity. We consider the stochastic perturbation, exogenous disturbance and the network-induced communication constraints in a whole framework of SMC design. The measurable output is adequately sampled for periodic computation of a designed event trigger. Network-induced delays are characterized in the transmission over a shared network communication from sensor to controller. An event-triggered zero-order-hold (ZOH) is employed to keep receiving and sending the delayed measurement for control updating, and a state observer is designed to estimate the system state and to facilitate the design of sliding surface. Then, based on the measurement and observer’s outputs, a novel SMC law is presented. The stochastic stability for the overall closed-loop system is analyzed, and the exogenous disturbance is attenuated in an sense. Furthermore, the presented event-triggered SMC methods are successfully applied to multi-loop control case considering shared communication limitation. Simulation results are provided to verify the effectiveness of the proposed design scheme.

This paper is concerned with the state estimation and sliding mode control problems for phase-type semi-Markovian jump systems. Using a supplementary variable technique and a plant transformation, a finite phase-type semi-Markov process has been transformed into a finite Markov chain, which is called its associated Markov chain. As a result, phase-type semi-Markovian jump systems can be equivalently expressed as its associated Markovian jump systems. A sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated Markovian jump systems satisfy the reaching condition. Moreover, an observer-based sliding mode control problem is investigated. Sufficient conditions are established for the solvability of the desired observer. Two numerical examples are presented to show the effectiveness of the proposed design techniques.

In this paper, the problems of stability analysis and stabilization are investigated for discrete-time two-dimensional (2-D) switched systems, which are formulated by the well-known Fornasini–Marchesini local state-space model. Firstly, by using the switched quadratic Lyapunov function approach, a sufficient stability condition is established for such systems under arbitrary switching signal. Then, the extended average dwell time technique combining with the piecewise Lyapunov function approach is developed, and it is utilized for the stability analysis of the 2-D switched systems for the restricted switching case. Based on the stability analysis results, sufficient conditions are presented to stabilize the 2-D switched systems. Finally, two examples are provided to illustrate the effectiveness of the proposed new design techniques.

This paper investigates the problem of Hankel-norm output feedback controller design for a class of T–S fuzzy stochastic systems. The full-order output feedback controller design technique with the Hankel-norm performance is proposed by the fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, a Henon map system is used to illustrate the effectiveness of the proposed techniques.