Exponential stability of a class of nonlinear singularly perturbed systems with delayed impulses

A class of nonlinear singularly perturbed systems with delayed impulses is considered. By delayed impulses we mean that the impulse maps describing the state's jumping at impulsive moments are dependent on delayed state variables. Assuming that each of two lower order subsystems possesses a Lyapunov function, exponential stability criteria for all small enough values of singular perturbation parameter are obtained. It turns out that the achieved exponential stability is robust with respect to small impulse input delays. A stability bound on perturbation parameter is also derived through using those Lyapunov functions. Additionally, for a class of singularly perturbed Lur'e systems with delayed impulses, an LMI-based method to determine stability and an upper bound of the singular perturbation parameter is presented. The results are illustrated by an example for the position control of a dc-motor with unmodelled dynamics.     

Fast finite time stability of stochastic nonlinear systems

This paper focus on fast finite time stability for a class of stochastic nonlinear systems. Firstly, a useful inequality, which will play a crucial role in the fast finite time stability in probability, is expanded on Bihari inequality. Then, the concept of fast finite time stability is discussed for stochastic nonlinear systems and an important theory concerned with fast finite time stability in probability is obtained. Next, a fast finite time state feedback controller can be subtle designed, which not only shortens the convergent time but also requires no large control effort. Three simulation examples are given to support our results of theoretical analysis.     

Stochastic input-to-state stability of random impulsive nonlinear systems

In this paper, the stochastic input-to-state stability is investigated for random impulsive nonlinear systems, in which impulses happen at random moments. Employing Lyapunov-based approach, sufficient conditions for the stochastic input-to-state stability are established based on the connection between the properties of system and impulsive intervals. Two classes of impulsive systems are considered: (1) the systems with single jump map; (2) the systems with multiple jump maps. Finally, some examples are provided to illustrate the effectiveness of the proposed results.     

Event-triggered control for nonlinear systems involving hybrid impulses

In this paper, we apply event-triggered control to nonlinear systems with impulses, and investigate the problem of ensuring globally exponential stability (GES) of the systems, where events and impulses may occur at different time. Moreover, two types of impulses (i.e., stabilizing and destabilizing) can coexist. On the basis of Lyapunov method and impulsive control theory, some sufficient conditions ensuring GES are derived, and the Zeno behaviour can be excluded. These conditions are presented in the form of linear matrix inequalities (LMI). In particular, inspired by average dwell-time methods, conditions for restriction of impulses are proposed, which guarantee GES of nonlinear systems involving single stabilizing and destabilizing or multiple impulses, respectively. Furthermore, the problem of designing event-triggered mechanism and control gains are solved by using LMI method. Lastly, two numerical simulation examples are given to represent the effectiveness of our results.     

Iterative learning control for linear delay systems with deterministic and random impulses

This paper investigates convergence of iterative learning control for linear delay systems with deterministic and random impulses by virtute of the representation of solutions involving a concept of delayed exponential matrix. We address linear delay systems with deterministic impulses by designing a standard P-type learning law via rigorous mathematical analysis. Next, we extend to consider the tracking problem for delay systems with random impulses under randomly varying length circumstances by designing two modified learning laws. We present sufficient conditions for both deterministic and random impulse cases to guarantee the zero-error convergence of tracking error in the sense of Lebesgue-p norm and the expectation of Lebesgue-p norm of stochastic variable, respectively. Finally, numerical examples are given to verify the theoretical results.     

Further results on asymptotic stability of linear neutral systems with multiple delays

The problem of asymptotic stability of linear neutral systems with multiple delays is addressed in this article. Using the characteristic equation approach, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. The structure information of the system matrices are taken into consideration in the proposed stability criteria, thus the conservatism found in the literature can be significantly reduced. Simple examples are given to demonstrate the validity of the criteria proposed and to compare them with the existing ones.     

Robust exponential stability of uncertain impulsive stochastic neural networks with delayed impulses

In this paper, by using Lyapunov functions, Razumikhin techniques and stochastic analysis approaches, the robust exponential stability of a class of uncertain impulsive stochastic neural networks with delayed impulses is investigated. The obtained results show that delayed impulses can make contribution to the stability of system. Compared with existing results on related problems, this work improves and complements ones from some works. Two examples are discussed to illustrate the effectiveness and the advantages of the results obtained.     

Further results on delay-dependent stability criteria of discrete systems with an interval time-varying delay

This paper deals with stability of discrete-time systems with an interval-like time-varying delay. By constructing a novel augmented Lyapunov functional and using an improved finite-sum inequality to deal with some sum-terms appearing in the forward difference of the Lyapunov functional, a less conservative stability criterion is obtained for the system under study if compared with some existing methods. Moreover, as a special case, the stability of discrete-time systems with a constant time delay is also investigated. Three numerical examples show that the derived stability criteria are less conservative and require relatively small number of decision variables.     

Improved stability theorems of random nonlinear time delay systems and their application

This paper focuses on stability theorems of random nonlinear time delay systems and their application. On the one hand, some noise-to-state practical stability theorems are improved for random nonlinear systems with time delay in this paper. Compared with the existing stability theorems, some strict constraints have been removed and the existing stability theorems can be viewed as special cases of the new established stability theorems in this paper. On the other hand, the state feedback tracking control problem is investigated to show the applicability of improved stability theorems in this paper.     

Networked feedback control for nonlinear systems with random varying delays

This paper discusses the controller synthesis problem of a nonlinear networked controlled system subject to delays in the measurement and actuation channels. The communication through the network also suffers non-stationary packet dropouts. The bounded nonlinearities in the plant state satisfy Lipschitz conditions. A Lyapunov function is developed for the closed-loop system considering dynamic output feedback and the resulting stabilization conditions are drawn in the form of linear matrix inequalities to ensure that the system is exponentially stable in the mean-square sense. The developed conditions are represented in the form of a convex optimization problem and the results are tested by simulation on a quadruple-tank process.     

General synchronization criteria for nonlinear Markovian systems with random delays

It is well known that control of Markovian systems is a difficult problem. This paper considers synchronization control of Markovian coupled nonlinear systems with random delays. A new control scheme is proposed. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained such that the coupled system can be asymptotically synchronized onto an isolated system. The synchronization criteria include classical mode-dependent and mode-independent results as special cases. The design method of the control gains is also given. Compared with mode-dependent and mode-independent control methods, our results are more practical and have lower conservatism, respectively. Numerical simulations are given to verify the effectiveness of the theoretical results.     

Recursive distributed fusion estimation for nonlinear stochastic systems with event-triggered feedback

This paper focus on the distributed fusion estimation problem for a multi-sensor nonlinear stochastic system by considering feedback fusion estimation with its variance. For any of the feedback channels, an event-triggered scheduling mechanism is developed to decide whether the fusion estimation is needed to broadcast to local sensors. Then event-triggered unscented Kalman filters are designed to provide local estimations for fusion. Further, a recursive distributed fusion estimation algorithm related with the trigger threshold is proposed, and sufficient conditions are builded for boundedness of the fusion estimation error covariance. Moreover, an ideal compromise between fusion center-to-sensors communication rate and estimation performance is achieved. Finally, validity of the proposed method is confirmed by a numerical simulation.     

Decentralized global stabilization for stochastic high-order feedforward nonlinear systems with time-varying delays

This paper studies the problem of decentralized stabilization for a class of large-scale stochastic high-order time-delay feedforward nonlinear systems. A series of delay-independent state feedback controllers is constructed, which is based on the approach of adding one power integrator. The stochastically global asymptotic stability (GAS) of the closed-loop system under the above-mentioned controllers is proved by Lyapunov–Krasovskii theorem and homogeneous domination approach. A simulation example is given to illustrate the effectiveness of the results of this paper.     

N-sigma stability of stochastic systems with sliding mode control

In this paper, sliding mode control for discrete time systems with stochastic noise in their input channel has been discussed. The idea of process control using control charts has influenced this new approach towards dealing with systems with stochastic noise. The new approach approximates the stochastic noise as a bounded uncertainty, similar to having bounds in the control charts for stochastic process control data. For discrete time systems, this results in a bounded stability in probability of the quasi sliding mode, which is referred to as the N-sigma bounded stability. The probability associated with the stability notions is not fixed and the control engineer may desire lower or higher degrees of stability in terms of this probability. Thus one has design flexibility while implementing the theory in practice, where one might have to adjust the desired degree of stability due to hardware limitations.     

Stabilization of Boolean control networks with stochastic impulses

This paper studies the stabilization problem of Boolean control networks with stochastic impulses, where stochastic impulses model is described as a series of possible regulatory models with corresponding probabilities. The stochastic impulses model makes the research more realistic. The global stabilization problem is trying to drive all states to reach the predefined target with probability 1. A necessary and sufficient condition is presented to judge whether a given system is globally stabilizable. Meanwhile, an algorithm is proposed to stabilize the given system by designing a state feedback controller and different impulses strategies. As an extension, these results are applied to analyze the global stabilization to a fixed state of probability Boolean control networks with stochastic impulses. Finally, two examples are given to demonstrate the effectiveness of the obtained results.     

Approximate controllability of nonlinear stochastic evolution systems with time-varying delays

In this paper, the approximate controllability of nonlinear stochastic evolution time-varying delay systems with preassigned responses is studied. The necessary conditions for controllability results of nonlinear systems are not associated with linear systems. No compactness assumptions are imposed in the main results.