Yan Jiang

This article addresses the problems of stability, ‐gain analysis, and periodic event‐triggered control of linear stochastic Markov jump systems with sampled measurements in both state and mode. An impulsive system framework is developed for designing dynamic periodic event‐triggering mechanisms, modeling, and analyzing the closed‐loop system with asynchronous control induced by mode sampling. A second‐order moment equation of the stochastic Markov jump system is first established to derive non‐conservative stability criteria for the time‐triggered case. Subsequently, mode‐dependent periodic polynomial/discretized Lyapunov functions are constructed to establish sufficient criteria for ‐gain properties and mean‐square exponential stability of the event‐triggered case. The co‐design of the controller and event‐triggering function is accomplished using linear matrix inequalities. Comparative numerical examples validate the theoretical results.

The global adaptive tracking problem for a class of high‐order nonlinear systems with time‐varying powers is considered in the frame of event‐triggered control and prescribed performance methods. A novel error transformation is introduced, distinct from existing approaches, eliminating the constraint on the initial state. To mitigate the risk of tracking error exceeding the prescribed range, a modified performance function is defined, allowing temporary deviation from the prescribed performance. An event‐triggered controller is formulated to ensure that the tracking error can converge to a predefined range within a specified settling time. The validity of the proposed scheme is illustrated by an example.

The finite‐time practical tracking problem is studied for a class of high‐order nonlinear systems with time‐varying full‐state constraints via event‐triggered control. In order to remove the feasibility conditions required by the traditional barrier Lyapunov functions (BLFs) method when dealing with state constraints, this paper introduces the nonlinear transformation functions (NTFs) for the states to transform the constrained system into an equivalent unconstrained system. An event‐triggered controller is designed with a wider application range and more suitable for the tracking control system by combining the switching threshold event‐triggered strategy. The purpose of reducing resource consumption is realized. The finite‐time stability of the closed‐loop system is proved by the finite‐time theory without breaking the state constraints. Finally, numerical and practical examples are given to verify the effectiveness of the proposed results.

This paper is devoted to stochastic convergence theorems for stochastic impulsive systems (SISs) and their application to discrete-time stochastic feedback control (DTSFC). A general stochastic Barbălat's lemma, that only requires that the concerned stochastic processes are almost surely integrable rather than absolutely integrable in the sense of expectation, for piecewise continuous adapted processes is first proposed, which is truly parallel to the deterministic one. As an extension of this lemma, a general stochastic convergence theorem is established for SISs, which can reveal and sufficiently apply the possible active contribution of the existing noise in the underlying system. To derive easy-to-check stability conditions, a series of LaSalle-type theorems and dwell-time-based conditions are established for stochastic stability/convergence of SISs. In contrast to preceding results, these stability criteria can not only characterize the stabilizing noise but also be applicable to SISs with both continuous and discrete unstable dynamics. Moreover, supported by the LaSalle-type theorems, the almost sure exponential stabilization problems by DTSFC in both time- and event-triggered control schemes are solved. Particularly, the proposed methods remove the global Lipschitz condition required in the literature and provide an explicit computation of the maximum allowable sampling period. Finally, four numerical examples with comparisons are used to illustrate the theoretical results.

The issue of adaptive fuzzy control for a category of high-order uncertain nonlinear systems is discussed in this paper. The time-varying full-state constraints are asymmetric, and the input is subjected to dead-zone. The asymmetric time-varying high-order barrier Lyapunov functions (BLFs) are constructed to depict the constraints characteristic and a controller design strategy is proposed. A dead-zone compensation mechanism is used to eliminate the influence of dead-zone input. Based on adding a power integrator technique and the adaptive control method, an adaptive state feedback controller is designed. As a consequence, all the constraints are not breached and the tracking error converges into a prescribed small region around the origin. Finally, a numerical example and a practical example are given to show the effectiveness of the proposed method.

Summary: This paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time‐ and event‐triggering impulses. Moment stability criteria and design methods of time‐ and event‐triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event‐triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time‐triggered guaranteed cost controller, however, with a larger, or at most equal, average inter‐transmission time. Based on the proposed framework of random‐impulses systems, a stochastic dynamic event‐triggered control strategy is proposed to solve sampled‐data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results.