Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method

Abstract

This paper focuses on the observer-based periodically intermittent control issue for linear systems by utilizing piecewise Lyapunov function method. Based on the concept of intermittent control, the description of an observer-based periodically intermittent controller is initially proposed. Then, stability of the corresponding periodically intermittent control system is analyzed by resorting to piecewise Lyapunov function method. Here, the so-called piecewise Lyapunov function means that Lyapunov function on control time intervals differs from the one on free time intervals. Besides, the existence of an observer-based periodically intermittent controller is converted into the feasibility of linear matrix inequalities. It is worth pointing out that, in comparison with an observer-based continuous controller, the designed observer-based periodically intermittent controller can still retain satisfactory performance with shorter control task execution time. Finally, an illustrative simulation example is given to show the validity and superiority of the result.

Formation‐Containment Control of Second‐Order Multiagent Systems via Intermittent Communication

“…The main idea of intermittent communication is shown in Figure 1 are not constants, which is different from [27,33,34].…”

“…Secondly, the leaders and followers in this paper reach the desired formationcontainment asymptotically within aperiodic intervals. However, intermittent communications were periodical in [27,33,34]. Thirdly, the leaders and followers suffer from the timevarying delays in this paper, but the reference [32], which investigated the consensus with intermittent communication, ignored the influence of communication delay.…”

“…Remark 9. Different form the references [27,33,34] that investigated the multiagent systems with periodical intermittent communication, Theorem 8 provides the conditions for the agents (6) and 7reaching the desired formationcontainment asymptotically within aperiodic intervals.…”

Pinning synchronization of nonlinear hybrid‐coupled complex networks with double time delays via aperiodically intermittent adaptive control

“…Thus, a lot of control methods such as linear or nonlinear feedback control, [4][5][6][7] adaptive control, [8][9][10][11][12] and sliding-mode control [13][14][15] have been studied extensively and deeply by researchers in various disciplines. Accordingly, these control methods can be continuous, [4][5][6][7][8][9][10][11][12][13][14][15] impulsive, [16][17][18][19] or intermittent [20][21][22][23][24][25][26][27][28][29][30][31][32] during the acquisition of complex network synchronization. Different from other control strategies, intermittent control is active in some time intervals and dormant in others, which shows that it has the feature of economy.…”

State‐dependent intermittent control of non‐linear systems

“…In [2], a periodically intermittent controller description is introduced to exponentially stabilise a class of non‐linear systems. In the framework of it, stabilisation and synchronisation issues are investigated for linear systems [3], time‐delay systems [4, 5], chaotic systems [6, 7], chaotic systems with time delays [8–11], networks with time delays [12, 13], neural networks [14–19], and complex networks [20–23]. Periodically intermittent time‐delay feedback control is utilised in [24] to exponentially synchronise Master‐Slave Lur'e system.…”