Huiying Liu’s research while affiliated with Dalian Maritime University and other places

This article addresses the input‐to‐state stability (ISS) problem for general discrete‐time impulsive and switched delayed systems coupled by delay‐dependent impulses. In our studied systems, the impulsive signal has a large degree of freedom, that is, the impulse effect can occur simultaneously with or different from the switching effect. A new Lyapunov–Krasovskii functional is proposed to deal with the delay effect of switching signal and impulsive jump, which is divided into the delay‐independent part and delay‐dependent part. A new concept named admissible edge‐dependent average impulsive interval (AED‐AII) is set up to characterize the impulse sequence relative to the admissible edge‐dependent average dwell time (AED‐ADT) concept of the switching signal. Based on AED‐ADT approach and AED‐AII technique, some improved sufficient outcomes guaranteeing ISS of discrete‐time impulsive and switched delayed systems are presented, respectively, for stabilizing and destabilizing delay‐dependent impulses. Meanwhile, the relationship among AED‐AII, AED‐ADT, the jump amplitude of switching signal and impulse signal at their respective discrete points, the decay rate of Lyapunov functional for system dynamics is connected to pursue ISS of the whole system. Compared with previous works, our setups enjoy the following characteristics: it thoroughly digs the influence of time delay existing in impulses and system dynamics on the function part of L‐K functional, which are less conservative relative to other works; the proposed AED‐ADT switching signals and AED‐AII jump signals cover a large set of hybrid systems. Two numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results.

This article addresses input‐to‐state stability (ISS) for general discrete‐time impulsive and switched delayed systems coupled with delayed impulses. In view of the multiple Lyapunov functionals and the subsequence method, some novel sufficient criteria pledging ISS are established. It is indicated that, the impulsive and switched delayed systems as an integral will be ISS if destabilizing impulses do not happen too frequently when the system flows are ISS with the impulse dynamics governing the delay‐dependent impulses not being ISS. Oppositely, when the impulse dynamics are ISS with the system flows not being ISS, the delayed impulses are demanded to happen intensively enough to eliminate the destabilizing influences of the system dynamics so that the ISS can be realized for the whole system. Especially, the whole system is ISS for arbitrary impulse time series when the system flows and the impulse dynamics are both ISS. The results obtained in this article, when compared with the prior consequences on similar problems, can deal with a large class of discrete delayed systems as the criteria not only apply to the cases of smaller delays than the dwell time bound, but also suitable to larger. Moreover, the acquired dwell time bound is more relaxed than existing ones in the sense that the dwell time constraints are independent of delay bounds and an extra parameter. In order to prove the effectiveness of the theoretical results, two examples are expressed with numerical simulations, in which the Chua's circuit system with delay‐dependent impulses is considered.

The main objective of this paper is to study the stability and stabilization problems for a class of impulsive switched systems with inappropriate impulsive switching signals under asynchronous switching. Here, “inappropriate” means that the impulse jump moment may be inconsistent with the asynchronous switching moment or the system switching moment. And “asynchronous” implies that the switching of controller modes lags behind that of system modes. The hybrid case of stable or unstable subsystems combining with stable and unstable impulses is explored. A novel Lyapunov-like function is constructed, which is discontinuous at some special instants, including the switching instants, the instants when the system modes and filter modes are matched, and the impulse jump instants. Based on the novel multiple Lyapunov-like function, the sufficient conditions for the closed loop system to be globally uniformly exponentially stable (GUES) are obtained with admissible edge-dependent switching signals. Furthermore, by excogitating the state-feedback switching controller, the gain matrix of the controller can be obtained by solving the linear matrix inequalities. Finally, two numerical examples and simulation results are given to prove the effectiveness of our main results.

In this paper, the asynchronous l 2 − l ∞ filtering problem is directed at a kind of discrete-time impulsive switched systems, where ‘asynchronous’ implies that there is a delay when switching occurs between filter modes and system modes. A novel Lyapunov function has been constructed. The inventiveness lies in discontinuity of Lyapunov-like function at both the switching time and the instant when the system modes and filter modes are matched. An improved inequality portraying the relationship among Lyapunov-like function, impulse, asynchronous phenomena and disturbance is built to pledge the l 2 − l ∞ performance. On the basis of directed graph, the novel Lyapunov function, the improved inequality and admissible edge-dependent average dwell time technology, some criteria suitable for proving the globally uniformly exponential stability of filtering error system are proposed with l 2 − l ∞ performance index, and the relevant filter can also be designed. Finally, three numerical examples show the availability of the obtained conclusions.