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In this paper, a novel constrained switching rule, called “time-triggered logical switching” (TTLS) is considered for switched logical dynamic systems (SLDSs). Compared with the general time-triggered switching, the activation mode of TTLS cannot be arbitrary and is pre-allocated according to the logic operation, which is more practical. The TTLS is described as an LDS, and according to the characteristics of LDS, the stability analysis of SLDSs with TTLS is converted into the stability analysis of SLDSs under the logical switching cycle sequences. Firstly, based on the equivalent algebraic form of SLDSs with TTLS, combining the Lyapunov theory of LDS with average dwell-time method, several sufficient conditions are put forward for ensuring the point stability of the considered SLDSs. Then, by defining the switching cycle invariant subset and constructing a new system, the set stability analysis of the original system is transformed into the point stability analysis of the new system, and further, the obtained results for the point stability analysis are applied to the set stability analysis. At last, the validity of obtained results is illustrated by simulation on gene and protein signaling activity patterns. [ABSTRACT FROM AUTHOR]

This paper considers weakly and strongly input-to-state stability (ISS) of a discrete-time time-varying delayed system with synchronous impulses and switches. By employing the uniformly asymptotically stable function and mode-dependent dwell time conditions, ISS criteria are derived using the Krasovskii and Razumikhin techniques. The time differences of the Krasovskii functionals or the Razumikhin functions can be mode-dependent and time-varying, which release constraints of some existing results. As subsequent results, we apply the derived ISS criteria to the multi-agent systems (MASs). Finally, two examples considering the quasi-consensus of MASs are given to verify the established results. [ABSTRACT FROM AUTHOR]

Although the cyber-physical system stability is widely studied, scholars focus more on system stability with communication time delay. Therein, grid-connected inverters with the digital control system are regarded as one simplest and typical cyber-physical system. Meanwhile, the switching/sampling frequency of the inverter is always selected as low as possible from an efficiency viewpoint, resulting in unavoidable delay time. This delay time is apt to cause the system instability, which is more prone to severity under weak grid. To this end, this paper provides a minimum switching/sampling frequency for grid-connected inverters. Firstly, the system impedance model with equivalent delay time is constructed, which is based on padé approximate approach. This equivalent delay time consists of three parts, i.e., sampling delay time in cyber/physical level, calculation delay time in cyber level and pulsewidth modulation delay time in physical level, which reflects the cyber-physical interaction impact. Furthermore, the stability forbidden criterion is applied to make the switching/sampling frequency solving process become Hurwitz matrix identification problem through space mappings. Based on these space mappings, an adaptive step search approach is adopted to obtain the minimum switching/sampling frequency. Finally, the proposed approach can well evaluate the system stability under different frequencies through simulation and experiment. [ABSTRACT FROM AUTHOR]

This paper studies stability for a class of switched descriptor systems with state bumpless transfer performance and input bumpless transfer performance. Since the state jump is inevitable for switched descriptor systems when a switching occurs, to restrain the amplitude of the state jump induced by switchings, for the first time, the state bumpless transfer performance of switched descriptor systems is defined. Moreover, when switching occurs, to avoid the abrupt and large control input signals change damaging the system, we are the first to introduce the input bumpless transfer control scheme for switched descriptor systems. Furthermore, by using multiple Lyapunov functions, a sufficient condition is put forward to make sure the state bumpless transfer performance, input bumpless transfer performance and asymptotical stability for the closed-loop systems. Meanwhile, the switching rule and the state feedback controller are co-designed. In the end, a multiple inputs numerical example and an application on the DC motor model are used to exhibit the merit and validity of the presented control scheme. [ABSTRACT FROM AUTHOR]

The almost sure finite-time sliding mode control issue is investigated for Markov jump systems. The switching asynchronism between the constructed controller and considered systems is studied. The influence of time-varying delays and disturbances on systems is fully considered, and the sliding mode controller design within a finite time interval is extended to the probability framework. First, the finite time interval is divided into the reaching and the sliding motion phases, and the almost sure finite-time boundedness is analyzed in both phases. Second, the sliding mode controller gain is determined by the provided linear matrix inequality-based criteria. Finally, a numerical example and DC-DC buck converter circuit example verify the effectiveness and less conservativeness of our method. [ABSTRACT FROM AUTHOR]

This article shows a focus on the positivity and stability of Cohen-Grossberg-type time-delay memristor neural networks. We start by providing the existence and unique theorem of solutions for time-delay memristor neural networks to the case of unbounded delays. It is clear to find that the discriminate criterion of the existence and uniqueness of solutions about the argumented system with unbounded delays plays an important role in other related unbounded time-delay systems. Leveraging the Lyapunov method along with memristor nonlinearity, sufficient and necessary conditions for positivity and stability of Cohen-Grossberg-type memristor neural networks under unbounded delays are gained. Our proposed criteria don’t need any strictly restrictive conditions. These theoretical results derived here will be helpful to understand the convergence performance of memristor electrical systems. [ABSTRACT FROM AUTHOR]