Event-triggered stabilisation for stochastic delayed differential systems with exogenous disturbances

In this paper, the practically input-to-state stabilization issue is considered for the stochastic delayed differential systems (SDDSs) with exogenous disturbances. To reduce the transmission frequency of the feedback control signal, the proposed SDDSs are stabilized by an event-triggered strategy. The concept of the practically input-to-state stability (ISS) is used to describe the dynamic performance of control target in the event-triggered schemes and exogenous disturbances. Besides, the considered SDDSs is stabilized by an event-triggered feedback controller which is represented by linear matrix inequalities. Moreover, lower bound of the interaction time of the event-triggered control method is obtained to avoid the Zeno behavior of the proposed event-triggering scheme. Finally, the effectiveness of the conclusion is verified by a numerical example.     

Sliding manifold design for linear systems with unmatched disturbances

This paper offers an efficient sliding manifold design method that minimizes the impact of unmatched disturbances onto SM dynamics and system accuracy. System sensitivity upon unmatched constant or slowly varying external disturbance vector is evaluated by the steady-state dependent criterion function. An infinite set of sliding manifolds that minimize the chosen optimization criterion is determined and a way of selecting a manifold out of that set that provides adopted SM dynamics is suggested. The proposed approach has been demonstrated on numerical examples and verified by simulations.     

Observer-based event-triggered sliding mode control for delayed systems with unknown disturbances

This paper develops the observer-based event-triggered sliding mode control strategy for delayed systems involving unknown disturbances. This strategy comprises a triggering rule which can effectively save resources and an observer-based control law which can drive the states of delayed systems into the practical sliding mode band in some finite time. Some sufficient conditions coupled with this control strategy are proposed to guarantee the robust performance of the delayed systems. Significant outcome of this strategy is that it can be applied to the case in which the disturbances are unmeasured or unknown. Finally, two numerical examples and its simulations are presented to show the performance of the systems and effectiveness of this control strategy.     

The ellipsoidal bound of reachable sets for linear neutral systems with disturbances

In this paper, we consider the problem of finding an ellipsoidal bound of reachable sets for neutral systems with bounded peak disturbances. Up to now, the result related to the ellipsoidal bound of reachable sets was rarely proposed for linear neutral systems. Based on the modified augmented Lyapunov-Krasovskii type functional, we obtain some delay-dependent results expressed in the form of matrix inequalities containing only one non-convex scalar. Furthermore, a modified integral inequality is used to remove the limitation on the variation rate of the delay. Numerical examples are given to indicate significant improvements over some existing results.     

Delay-independent stabilization of linear systems with time-varying delayed state and uncertainties

The problem of robust stabilization for a class of dynamic systems with time-varying state delay as well as parametric and input uncertainties is considered in this paper. Several delay-independent stabilizability criteria and memoryless state feedback controllers are presented to guarantee the asymptotic stability of the closed-loop uncertain time-delay systems. It is shown that if all uncertainties and delay terms are matched, then the mentioned systems can always be stabilized, or can be stabilized with a specified decaying rate.     

New results on reachable sets bounding for delayed positive singular systems with bounded disturbances

This paper addresses the reachable sets bounding problem for time-delay positive singular systems subject to bounded disturbances. The time delays in the considered systems are assumed to be time-varying. Both invariant and time-varying singular systems are investigated in this paper. Existence conditions of componentwise ultimate bounds of the state vector of considered systems are derived and given in terms of the spectral abscissa of the system matrices, which are easy to be checked. The obtained results are demonstrated by two numerical examples.     

Distributed disturbance observer based consensus control for linear multi-agent systems with mismatched disturbances

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws.     

Full-order and reduced-order observers for linear parameter-varying systems with one-sided Lipschitz nonlinearities and disturbances using parameter-dependent Lyapunov function

In this study, H_∞ full-order and reduced-order observers are designed for a class of linear parameter-varying (LPV) systems with one-sided Lipschitz nonlinearities and disturbances. Parameter-dependent Lyapunov function is used to analyze the robust stability of the proposed observers. Three practical examples are used to demonstrate the usefulness of the proposed observers. Simulation and experimental results indicate that the proposed observers work well.     

Scale-based cluster formation for multi-agent systems with mismatched disturbances

This paper studies scale-based cluster formation problem of multi-agent system (MASs) under mismatched disturbances. A distributed sliding mode control with a disturbance observer is proposed to solve the aforementioned problem in the leaderless and leader-follower cases. The proposed control strategy provides satisfactory robust performance under mismatched disturbances and is thus more applicable to complicated formation control tasks. Finally, simulation results are provided to justify the validity of the proposed method.     

Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations

This paper investigates the stability robustness of linear output feedback systems with both time-varying structured (elemental) and unstructured (norm-bounded) parameter uncertainties as well as delayed perturbations by directly considering the mixed quadratically coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, two new sufficient conditions are proposed for ensuring that the linear output feedback systems with delayed perturbations as well as both time-varying structured and unstructured parameter uncertainties are asymptotically stable. The corresponding stable region, that is obtained by using the proposed sufficient conditions, in the parameter space is not necessarily symmetric with respect to the origin of the parameter space. Two numerical examples are given to illustrate the application of the presented sufficient conditions, and for the case of only considering both the delayed perturbations and time-varying structured parameter uncertainties, it can be shown that the results proposed in this paper are better than the existing one reported in the literature.     

Continuous fixed-time convergent regulator for dynamic systems with unbounded disturbances

This paper presents a novel continuous fixed-time convergent control law for dynamic systems in the presence of unbounded disturbances. A continuous fixed-time convergent control is designed to drive all states of a multi-dimensional integrator chain at the origin for a finite pre-established (fixed) time, using a scalar input. The fixed-time convergence is established and the uniform upper bound of the settling time is computed. The designed control algorithm is applied to fixed-time stabilization of two mechatronic systems, a cart inverted pendulum and a single machine infinite bus turbo generator with main steam valve control.     

Robust multi-tracking of heterogeneous multi-agent systems with uncertain nonlinearities and disturbances

A robust multi-tracking problem is solved for heterogeneous multi-agent systems with uncertain nonlinearities and disturbances. The nonlinear function satisfies a Lipschitz condition with a time-varying gain, the integral of which is bounded by a linear function. A distributed impulsive protocol is proposed, where the position data and velocity data of desired trajectories are needed only at sampling instants. Based on the system decomposition technique, the error dynamic system of achieving multi-tracking is decomposed into two impulsive dynamic systems with vanishing perturbation and nonvanishing perturbation, respectively. Constructing a nominal model, then the multi-tracking problem is converted into the stability of impulsive dynamic system with nonvanishing perturbation under some conditions. It is proved that the proposed impulsive protocol is robust enough to solve the multi-tracking problem. Numerical examples are presented to illustrate the effectiveness of our theoretical results.     

Composite fault-tolerant control with disturbance observer for stochastic systems with multiple disturbances

In this paper, a composite fault tolerant control (CFTC) with disturbance observer scheme is considered for a class of stochastic systems with faults and multiple disturbances. The disturbances are divided into two parts. One represents the stochastic disturbance with partial known information which is formulated by an exogenous system. The other is independent Wiener process. A stochastic disturbance observer is designed to estimate exogenous disturbance. To make the first type of disturbance can be rejected and the fault can be diagnosed, a composite fault diagnosis observer with disturbance observer is constructed. Furthermore, a composite fault-tolerant controller is proposed to compensate disturbances and faults. Finally, simulation examples are given to demonstrate the feasibility and effectiveness of the proposed scheme.     

Detection-estimation strategies for delayed systems with unavailable packet sequence

In this paper, we study the problem of remote state estimation on networks with random delays and unavailable packet sequence due to malicious attacks. Two maximum a posteriori (MAP) schemes are proposed to detect the unavailable packet sequence. The first MAP strategy detects the packet sequence using data within a finite time horizon; the second MAP strategy detects the packet sequence by a recursive structure, which effectively reduces the computation time. With the detected packet sequence, we further design a linear minimum mean-squared error (LMMSE) estimation algorithm based on smoothing techniques, rather than using the classic prediction and update structure. A wealth of information contained in the combined measurements is utilized to improve the estimation performance. Finally, the effectiveness of the proposed algorithms is demonstrated by simulation experiments.     

Event-triggered delayed impulsive control for nonlinear systems with applications

In this paper, we investigate the Lyapunov stability for general nonlinear systems by means of the event-triggered impulsive control (ETIC), in which the delayed impulses are greatly taken into account. On the basis of impulsive control theory, a set of Lyapunov-based sufficient conditions for uniform stability and asymptotic stability of the addressed system are obtained in the framework of event triggering, under which Zeno behavior is excluded. It is shown that our results depend on the event-triggering mechanism (ETM) and the time delays. Then the mentioned results are applied to synchronization of chaotic systems and moreover, a kind of impulsive controllers is designed in form of linear matrix inequality (LMI), where the delayed impulsive control can be activated only when events happen. In the end, to illustrate the validity of the mentioned theoretical results, we present a numerical example.     

Block-balancing of linear systems

A generalization of balanced realizations called “block-balanced” realizations is introduced. A sufficient condition to obtain a block-balanced realization is given and computational advantages over the balanced realizations are pointed out. It is shown that all the properties of balanced realizations are preserved in block-balanced realizations. Finally, a new norm condition to obtain a reduced model is provided.     

Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances

In this paper we study stochastic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. Based on the Lyapunov stability theory, the properties of a Brownian motion, the generalized Itô's formula and linear matrix inequalities technique, some new delay-dependent conditions are derived to guarantee the stochastically asymptotic stability of the trivial solution or zero solution. In particular, the activation functions in this paper depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. Also, time delays proposed in this paper comprise both constant delays and time-varying delays. Moreover, the derivative of time delays is allowed to take any value. Therefore, the results obtained in this paper are less conservatism and generalize those given in the previous literature. Finally, two numerical examples and their simulations are used to show the effectiveness of the obtained results.     

Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances

In motor system control design, a single controller is usually employed to simultaneously control two or more motors for saving costs, which also achieves the computational simplification of control. In practical Hamiltonian systems control, more systems also need to be stabilized by a single controller under some working conditions. Thus, this paper studies simultaneous stabilization problem of two nonlinear Port-controlled Hamiltonian (PCH) systems with disturbances by a composite controller. Based on the Hamiltonian structure properties, two PCH systems are combined together to generate an augmented PCH system by utilizing output feedbacks firstly. Then, to estimate disturbances effectively, it is essential to design a nonlinear disturbance observer (NDOB) and the estimate is employed to feedforward compensate the effects of disturbances. Next, combining the output feedback part and the disturbance compensation part together, a simultaneous stabilization controller is developed. Subsequently, it is proved that the closed-loop system under the proposed controller is asymptotically stable. Finally, an example with simulations reveals that the proposed method is effective.