Integral Input-to-State Stability of Nonlinear Time-Delay Systems with Delay-Dependent Impulse Effects

This paper studies integral input-to-state stability (iISS) of nonlinear impulsive systems with time-delay in both the continuous dynamics and the impulses. Several iISS results are established by using the method of Lyapunov-Krasovskii functionals. For impulsive systems with iISS continuous dynamics and destabilizing impulses, we derive two iISS criteria that guarantee the uniform iISS of the whole system provided that the time period between two successive impulse moments is appropriately bounded from below. Then we provide an iISS result for systems with unstable continuous dynamics and stabilizing impulses. For this scenario, it is shown that the iISS properties are guaranteed if the impulses occur frequently enough. For impulsive systems with stabilizing impulses and stable continuous dynamics for zero input, we obtain an iISS result which shows that the entire system is uniformly iISS over arbitrary impulse time sequences. As applications, iISS properties of a class of bilinear systems are studied in details with simulations to demonstrate the presented results

Event-Triggered Stabilization of Linear Time-Delay Systems via Halanay-Type Inequality

This paper studies the event-triggered control problem for time-delay systems. A novel event-triggering scheme is proposed to exponentially stabilize a class of linear time-delay systems. By employing a new Halanay-type inequality and the Lyapunov function method, sufficient conditions on the design of control gain and selection of parameters in the proposed event-triggering scheme are derived to both ensure the exponential stability of the closed-loop system and exclude Zeno behavior. Two examples are given to demonstrate the effectiveness of the theoretical result

Excluding Zeno Behaviour in Event-Triggered Time-Delay Systems by Impulsive Controls

In this paper, we study the problem of event-triggered control for stabilization of general nonlinear time-delay systems. Based on a Razumikhin-type input-to-state stability result for time-delay systems, we propose an event-triggered control algorithm to stabilize nonlinear time-delay systems. In order to exclude the Zeno behaviors, we combine a novel impulsive control mechanism with the proposed event-triggered strategy; in this sense, our proposed algorithm is a hybrid impulsive and event-triggered strategy. We then obtain sufficient conditions for the stabilization of the nonlinear control systems with time-delay by using the Lyapunov method and Razumikhin technique. Numerical simulations are provided to show the effectiveness of our theoretical results

Event-Triggered Control for Discrete-Time Delay Systems

This study focuses on event-triggered control of nonlinear discrete-time systems with time delays. Based on a Lyapunov-Krasovskii type input-to-state stability result, we propose a novel event-triggered control algorithm that works as follows. The control inputs are updated only when a certain measurement error surpasses a dynamical threshold depending on both the system states and the evolution time. Sufficient conditions are established to ensure that the closed-loop system maintains its asymptotic stability. It is shown that the time-dependent portion in the dynamical threshold is essential to derive the lower bound of the times between two consecutive control updates. As a special case of our results, we demonstrate the performance of the designed event-triggering algorithm for a class of linear control systems with time delays. Numerical simulations are provided to demonstrate the effectiveness of our algorithm and theoretical results

Impulsive Control of Dynamical Networks

Dynamical networks (DNs) consist of a large set of interconnected nodes with each node being a fundamental unit with detailed contents. A great number of natural and man-made networks such as social networks, food networks, neural networks, WorldWideWeb, electrical power grid, etc., can be effectively modeled by DNs. The main focus of the present thesis is on delay-dependent impulsive control of DNs. To study the impulsive control problem of DNs, we firstly construct stability results for general nonlinear time-delay systems with delayed impulses by using the method of Lyapunov functionals and Razumikhin technique. Secondly, we study the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Then, a novel hybrid consensus protocol with dynamically changing interaction topologies is designed to take the time-delay into account in both the continuous-time communication among agents and the instant information exchange at discrete moments. We also study the consensus problem of networked multi-agent systems. Distributed delays are considered in both the agent dynamics and the proposed impulsive consensus protocols. Lastly, stabilization and synchronization problems of DNs under pinning impulsive control are studied. A pinning algorithm is incorporated with the impulsive control method. We propose a delay-dependent pinning impulsive controller to investigate the synchronization of linear delay-free DNs on time scales. Then, we apply the pinning impulsive controller proposed for the delay-free networks to stabilize time-delay DNs. Results show that the delay-dependent pinning impulsive controller can successfully stabilize and synchronize DNs with/without time-delay. Moreover, we design a type of pinning impulsive controllers that relies only on the network states at history moments (not on the states at each impulsive instant). Sufficient conditions on stabilization of time-delay networks are obtained, and results show that the proposed pinning impulsive controller can effectively stabilize the network even though only time-delay states are available to the pinning controller at each impulsive instant. We further consider the pinning impulsive controllers with both discrete and distributed time-delay effects to synchronize the drive and response systems modeled by globally Lipschitz time-delay systems. As an extension study of pinning impulsive control approach, we investigate the synchronization problem of systems and networks governed by PDEs

A Note on Stability of Event-Triggered Control Systems with Time Delays

This note studies stability of event-triggered control systems with the event-triggered control algorithm proposed in [1]. We construct a novel Halanay-type inequality, which is used to show that sufficient conditions of the main results in [1] ensure stability of the event-triggered control systems that was missing in [1]. It is also shown that a positive parameter in the proposed event-triggering condition in [1] can be freely selected to exclude Zeno behavior from the event-triggered control system. An illustrative example is investigated to demonstrate the theoretical results of this study with numerical simulations. [1] K. Zhang, B. Gharesifard, and E. Braverman, Event-triggered control for nonlinear time-delay systems, IEEE Transactions on Automatic Control, vol. 67, no. 2, pp. 1031-1037, 2022

Anti-Tumor Activity of a Novel Protein Obtained from Tartary Buckwheat

TBWSP31 is a novel antitumor protein that was isolated from tartary buckwheat water-soluble extracts. The objective of this paper was to investigate the anti-proliferative effects of TBWSP31 on breast cancer Bcap37cells and to explore its possible mechanism. After treatment of Bcap37 cells with TBWSP31, typical apoptotic morphological changes were observed by inverted microscopy and scanning electron microscopy (SEM), such as detachment from the culture plate, change to a round shape, cell shrinkage, the absence of obvious microvilli, plasma membrane blebbing, and formation of apoptotic bodies. Cell-cycle analysis revealed that treatment with TBWSP31 resulted in a G0/G1 arrest and prevented the cells from growing from G0/G1 phase to S phase, which was most prominent at 48 h. The expression of bcl-2 and Fas were detected quantitatively by FCM, which showed that TBWSP31 induced-apoptosis may be involved with the participation of Fas and bcl-2. These results suggest that TBWSP31 is a potential antitumor compound and that apoptosis induced by TBWSP31 is a key antitumor mechanism

Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results

Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results