Event-triggered sliding mode control for singular systems with disturbance

This paper investigates the event-triggered sliding mode control (SMC) problem for singular systems with disturbance. Firstly, an event-triggered sliding mode control law is designed to guarantee the reachability of sliding surface. Different from the related methods, in order to deal with the difficulty caused by event-triggered SMC strategy, a novel Lemma is proposed in this paper. Secondly, the admissibility of sliding motion is presented, which is used to solve the controller gain. Then, a positive lower bound of the inter execution time can be guaranteed and the Zeno behavior is avoided. Finally, two simulation examples are presented to show the effectiveness of derived theoretical results.     

A generic design methodology for sliding mode control of switched systems

The aim of this paper is to present a generic methodology to design sliding mode controllers for multivariable switched systems affine in control such as dc–dc power converters. An original formulation of the so-called reachability condition, suitable for this class of systems, is established. Based on the choice of a Lyapunov-like function and parameterized by a single weighting matrix, it allows several kinds of control strategies to be derived, namely conventional piecewise continuous strategies as well as discrete (Boolean) strategies. Its application to the important subclass of linear time invariant systems is investigated more specifically. In the Boolean case, the present approach is also compared to another hybrid one called the stabilizing approach. Eventually, its efficiency as a design methodology, as well as the performance of the resulting control, are shown by simulating it on non-trivial examples of power converters.     

Finite-time filtering for switched linear systems with a mode-dependent average dwell time

This study considers the problem of finite-time filtering for switched linear systems with a mode-dependent average dwell time. By introducing a newly augmented Lyapunov–Krasovskii functional and considering the relationship between time-varying delays and their upper delay bounds, sufficient conditions are derived in terms of linear matrix inequalities such that the filtering error system is finite-time bounded and a prescribed noise attenuation level is guaranteed for all non-zero noises. Thus, a finite-time filter is designed for switched linear systems with a mode-dependent average dwell time. Finally, an example is given to illustrate the efficiency of the proposed methods.     

Model predictive control for switched systems with a novel mixed time/event-triggering mechanism

This paper investigates observer-based model predictive control (MPC) for switched systems with a mixed time/event-triggering mechanism. The problem of predictive control that can achieve receding horizon optimization is considered and solved by minimizing an upper bound of the quadratic cost function. Since the system state may not be fully measured in practice, state observers are employed to estimate. A mixed mechanism including adaptive event-triggering and time-triggering is proposed, which can be switched determined by a threshold describing system performance to better balance system resource utilization and performance requirements. Then, a closed-loop switched system subject to networked-time-delay is modeled. Piecewise Lyapunov function technique and average dwell time approach are utilized to ensure asymptotical stability. Afterwards, MPC controller construction problem is turned into a LMIs feasibility problem. A new solving method of sufficient conditions for co-design of the state observers, feedback controllers and mixed triggering mechanism is derived. Lastly, simulation examples illustrate the correctness and advantages of research content.     

Continuous output integral sliding mode control for switched linear systems

A continuous output integral sliding mode robustification methodology for switched uncertain linear time invariant systems with state-dependent location transitions and dwell time is presented. The robustifying methodology is based on the adjustment of the super-twisting algorithm gains to assure the convergence time and the attenuation of the chattering. The use of the adjusted STA allows to reconstruct the states theoretically exactly before half of the dwell time without the usage of filters, via a continuous cascade observer. Moreover, it allows to generate a continuous control signal that is turn on after the observer has converged, guaranteeing theoretically exact compensation of the matched uncertainties/perturbations before the dwell time.     

Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control

-In this paper, we investigate the synchronization problems of chaotic fuzzy cellular neural networks with time-varying delays. To overcome the difficulty that complete synchronization between non-identical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of non-identical chaotic fuzzy cellular neural networks with time-varying delays, where the parameters and activation functions are mismatched. This research demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

Robust reliable control for uncertain switched nonlinear systems with time delay under asynchronous switching

This paper investigates the problem of robust reliable control for a class of switched nonlinear systems with time delay and actuator failures under asynchronous switching. When the switching instants of the controller experience delays with respect to those of the system, a kind of reliable controller design method is proposed, and the dwell time approach is utilized for the stability analysis. Sufficient conditions for the existence of the reliable controller are formulated in terms of a set of LMIs. Then the proposed approach is extended to take into account switched delay systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Finite-time L1 control for positive switched linear systems with time-varying delay

This paper is concerned with the problem of finite-time L₁ control for a class of positive switched linear systems with time-varying delay. Firstly, by using the average dwell time approach, sufficient conditions which can guarantee the L₁ finite-time boundedness of the underlying system are given. Then, in virtue of the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with L₁-gain performance. All the obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be solved conveniently. Finally, an example is given to illustrate the efficiency of the proposed method.     

Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays

In this paper, the stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks (GRNs) with mixed time delays (discrete time delays and distributed time delays) and stochastic perturbations. The main purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable. By utilizing a more general Lyapunov-Krasovskii functional based on the idea of “delay decomposing” and the LMI (linear matrix inequality) technique, we derive sufficient delay-dependent conditions ensuring the asymptotically stability of the GRNs with mixed time delays and noise perturbations in terms of LMI. Finally, simulation examples are exploited to illustrate the effectiveness of the developed theoretical results.     

Robust state estimation for Markov jump genetic regulatory networks based on passivity theory

In this article, the robust state estimation problem for Markov jump genetic regulatory networks (GRNs) based on passivity theory is investigated. Moreover, the effect of time‐varying delays is taken into account. The focus is on designing a linear state estimator to estimate the concentrations of the mRNAs and the proteins of the GRNs, such that the dynamics of the state estimation error can be stochastically stable while achieving the prescribed passivity performance. By applying the Lyapunov–Krasovskii functional method, delay‐dependent criteria are established to ensure the existence of the mode‐dependent estimator in the form of linear matrix inequalities. Based on the obtained results, the parameters of the desired estimator gains can be further calculated. Finally, a numerical example is given to illustrate the effectiveness of our proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 214–223, 2016     

An improved robust delay-dependent stability criterion for genetic regulatory networks with interval time delays

This paper proposes an improved robust delay-dependent criterion for stability of genetic regulatory networks with delays which vary in an interval. A modified Lyapunov-Krasovskii functional is used to derive a sufficient condition in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. The derived stability criterion is less conservative than ones in the literature. A numerical example and simulation results show the effectiveness of the proposed method.     

Stochastic Stability Analysis for Switched Genetic Regulatory Networks with Interval Time-Varying Delays Based on Average Dwell Time Approach

In this article, the problem of stochastic stability analysis for switched stochastic genetic regulatory networks with interval time-varying delays based on average dwell time approach is investigated. By constructing the piecewise Lyapunov-Krasovskii functional, delay-dependent stability conditions are derived by using free-weighting matrix and convex combination approach. The derived stability conditions are expressed in terms of linear matrix inequalities which can be easily solved by using the MATLAB LMI control toolbox. Finally, numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed theoretical results.     

Synchronization of master-slave markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin's formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.     

Sliding mode control experiments of uncertain dynamical systems with time delay

This article presents the simulation and experimental studies for the nonlinear time-delayed dynamical systems with uncertainties. A rotary flexible joint made by Quanser is chosen as the model system to investigate the method for sliding mode control design. We considered the geometric nonlinearity of the flexible joint consisting of two linear springs. The system is assumed to have constant delay time and uncertain parameters with known upper and lower bounds. We also design an optimal sliding surface for the sliding mode control. Simulations and experiments are carried out to demonstrate the utility of the control method. Finally, the results from the simulations and experiments are in excellent agreement.     

State estimation for Markovian jumping genetic regulatory networks with random delays

In this paper, the state estimation problem is investigated for stochastic genetic regulatory networks (GRNs) with random delays and Markovian jumping parameters. The delay considered is assumed to be satisfying a certain stochastic characteristic. Meantime, the delays of GRNs are described by a binary switching sequence satisfying a conditional probability distribution. The aim of this paper is to design a state estimator to estimate the true states of the considered GRNs through the available output measurements. By using Lyapunov functional and some stochastic analysis techniques, the stability criteria of the estimation error systems are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable. Then, the explicit expression of the desired estimator is shown. Finally, a numerical example is presented to show the effectiveness of the proposed results.