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1.
An upper bound for the singular perturbation parameter is found for the uniform asymptotic stability of singularly perturbed linear time-varying systems.  相似文献   

2.
The robust stability problem for linear time-delay systems with general linear delayed impulses is investigated. Different from the previous results, the impulse-delays are allowed to be larger than the impulse period. An auxiliary state variable is introduced to construct an augmented model of the impulsive system, under which the discrete dynamics introduced by impulse-delays can be highlighted. A novel piecewise Lyapunov functional is introduced to analyze the stability of the augmented model. This functional is continuous along the trajectories of the augmented model, and is not required to be positive-definite at non-impulse instants. LMI-based exponential stability conditions are derived, which depend on both the impulse-dwell-time and the impulse-delay-interval. Numerical examples show that the obtained stability criteria are able to handle the benefit/harmful impulse-delays.  相似文献   

3.
The stabilization of a class of singularly perturbed linear time-varying systems is considered through the separate stabilization of two lower dimensional subsystems in two different time-scales. A composite stabilizing controller is synthesized from the separate stabilizing controllers of the two subsystems, the mutually independent gains of which do not require knowledge of the small singular perturbation parameter.  相似文献   

4.
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.  相似文献   

5.
This work aims to analyze the exponential stability of a non-linear impulsive neutral stochastic delay differential system. In this study, impulse perturbation is considered a delay-dependent state variable. The solution of the delay-dependent impulsive neutral stochastic delay differential system is associated with the solution of the system without impulses. First, we developed a relation connecting the solution of the neutral stochastic delay differential system without impulses and the solution of the corresponding system with impulses. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive system. Finally, the achieved theoretical results are illustrated for applying the Malthusian single species neutral stochastic delay population model with immigration impulses.  相似文献   

6.
This paper investigates the security control problem for a class of two-time-scale cyber-physical systems (TTSCPSs) with multiple transmission channels under the denial-of-service (DoS) attacks. A linear TTSCPSs model is first proposed with slow and fast transmission channels, which correspond to slow and fast physical components in terms of their communicating capacities and sampling rates. The measurement data-packets are transmitted via slow and fast transmission channels which are compromised by asynchronous DoS attacks. A novel composite controller depending on the singular perturbation parameter (SPP) is formulated and corresponding switching laws are designed to achieve certain resilience against DoS attacks. Then, by establishing a SPP-dependent Lyapunov function, sufficient conditions are obtained on the duration and frequency of the DoS attacks, such that, for any SPP less than or equal to a predefined upper bound, the input-to-state stability can be guaranteed for the closed-loop TTSCPSs. Finally, a networked DC motor control system is employed to demonstrate the effectiveness of the proposed security control algorithm.  相似文献   

7.
This paper considers the problem of stability of a singularly perturbed system and of finding an upper bound for the parameter when the order of the system changes as a result of parameter perturbation. By means of the contraction mapping technique, conditions have been derived for determining explicitly the range of parameter perturbation such that both bounded-input-bounded-output and asymptotic stabilities are insured. In addition, bounds of the state and output of the singularly perturbed system can be found. Two examples are given to illustrate the application and significance of the results.  相似文献   

8.
In this paper, an auxiliary model-based nonsingular M-matrix approach is used to establish the global exponential stability of the zero equilibrium, for a class of discrete-time high-order Cohen–Grossberg neural networks (HOCGNNs) with time-varying delays, connection weights and impulses. A new impulse-free discrete-time HOCGNN with time-varying delays and connection weights is firstly constructed, and the relationship between the solutions of original systems and new HOCGNNs is indicated by a technical lemma. From which, the global exponential stability criteria for the zero equilibrium are derived by using an inductive idea and the properties of nonsingular M-matrices. The effectiveness of the obtained stability criteria is illustrated by numerical examples. Compared with the previous results, this paper has three advantages: (i) The Lyapunov–Krasovskii functional is not required; (ii) The obtained global exponential stability criteria are applied to check whether a matrix is a nonsingular M-matrix, which can be conveniently tested; (iii) The proposed approach applies to most of discrete-time system models with impulses and delays.  相似文献   

9.
This paper deals with the problem of stabilization for a class of hybrid systems with time-varying delays. The system to be considered is with nonlinear perturbation and the delay is time varying in both the state and control. Using an improved Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a memoryless switched controller design for exponential stabilization of switched systems is proposed. The conditions for the exponential stabilization are presented in terms of the solution of matrix Riccati equations, which allow for an arbitrary prescribed stability degree.  相似文献   

10.
Sufficient conditions are obtained to guarantee the asymptotic stability of a class of non-linear singularly perturbed systems. A procedure for constructing a Lyapunov function for such a class of systems is given, and a clearly defined domain of attraction of the equilibrium is obtained. A stabilizing feedback control for such systems is also proposed.  相似文献   

11.
This study addresses the exponential stability and positive stabilization problems of impulsive positive systems (IPSs) with time delay. Specially, three types of impulses, namely, disturbance, “neutral”, and stabilizing impulses, are considered. For each type of impulsive effect, the exponential stability criterion is established utilizing the Lyapunov–Razumikhin techniques. Moreover, on the basis of the obtained stability results, the state-feedback controller design problem is investigated to positively stabilize the IPSs with time delay under different types of impulsive effects. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.  相似文献   

12.
This paper deals with the exponential stability problem for a class of neutral singular systems with Markovian jump parameters. The considered systems involve time-varying delays not only in their state but also in their derivatives of state. By using the Lyapunov–Krasovskii functional method, some sufficient conditions are derived, which ensure that the considered systems are regular, impulse-free and exponentially stable. Finally, some numerical examples are employed to demonstrate the effectiveness of the obtained approaches.  相似文献   

13.
This paper is concerned with state feedback stabilization of discrete-time switched singular systems with time-varying delays existing simultaneously in the state, the output and the switching signal of the switched controller. On the basis of equivalent dynamics decomposition and Lyapunov–Krasovskii method, exponential estimates for the response of slow states of the closed-loop subsystems running in asynchronous and synchronous periods are first given. Exponential estimates for the response of fast states are also provided by establishing an analytic equation to solve the fast states and using some algebraic techniques. Then, by employing the obtained exponential estimates and the piecewise Lyapunov function approach with average dwell time (ADT) switching, sufficient conditions for the existence of a class of stabilizing switching signals and state feedback gains are derived, which explicitly depend on upper bounds on the delays and a lower bound on the ADT. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.  相似文献   

14.
In this work, impulsive stabilization problems of discrete-time switched linear systems with time-varying delays are studied. The sequence of impulsive instants is nearly-periodic, i.e., it is close to a periodic impulse and the distance between them is an uncertain bounded term. A time-varying Lyapunov function is introduced to characterize the information of delays, switching signals and impulses, and a stability criterion LMI-based is obtained without any restrictions on the stability of the subsystems. Several design schemes of reduced-order/full-order impulsive controllers with or without time-varying delays are developed. Finally, three numerical examples are provided to illustrate the effectiveness of the established results.  相似文献   

15.
In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.  相似文献   

16.
This paper is concerned with the dynamic quantized control for switched fuzzy systems with singular perturbation and an improved event-triggered protocol. Essentially apart from the transition probabilities, the nonhomogeneous sojourn probabilities are employed to characterize the dynamic behavior of switched fuzzy singularly perturbed systems based on a deterministic switching signal. Benefiting from the dynamic quantization parameter, the quantization-based event-triggered protocol is presented, thereby decreasing the communication load. Based on the hidden Markov model, a novel event-triggered asynchronous control law is built. Finally, two examples are shown to clarify the practicality of the obtained results.  相似文献   

17.
The design problem of collocated feedback controllers is addressed in this paper for a class of semi-linear distributed parameter systems described by parabolic partial differential equation (PDE), where a finite number of local actuators and sensors are intermittently distributed in space. A Lyapunov direct method for the exponential stability analysis of the resulting closed-loop system is first presented for the system, in which the first mean value theorem for integration and the Wirtinger's inequality are employed. The corresponding stabilization condition is then derived through the analysis result. Finally, the proposed design method is implemented on the feedback control of a fisher equation and its effectiveness is evaluated through simulation results.  相似文献   

18.
《Journal of The Franklin Institute》2022,359(18):10785-10812
  相似文献   

19.
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.  相似文献   

20.
The property of input-to-state stability (ISS) of inertial memristor-based neural networks with impulsive effects is studied. Firstly, according to the characteristics of memristor and inertial neural networks, the inertial memristor-based neural networks are built. Secondly, based on the impulsive control theory, the average impulsive interval approach, Halanay differential inequality, Lyapunov method and comparison property, some sufficient conditions ensuring ISS of the inertial memristor-based neural networks under impulsive controller are derived. In this paper, we consider two types of impulse, stabilizing impulses and destabilizing impulses. When the inertial memristor-based neural networks are originally not ISS, by choosing a suitable lower bound of the average impulsive interval, the stabilizing impulses can be used to stabilize the inertial memristor-based neural networks. On the contrary, the inertial memristor-based neural networks are originally ISS, by restricting the upper bound of the average impulsive interval, the ISS of inertial memristor-based neural networks with destabilizing impulses can be ensured. Finally, numerical results are presented to illustrate the main results.  相似文献   

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