Synchronization of singular switched complex networks via impulsive control with all nonsynchronized subnetworks

Abstract

Summary This paper studies impulsive synchronization of a class of nonlinear singular switched complex networks (SSCNs). With the aid of discretized Lyapunov function method and the matrix generalized inverse technique, an impulsive controller is designed, which works on both the slow and the fast state variables to synchronize SSCNs at impulsive instant. Based on the designed controller, it is shown that the synchronization of SSCNs is achieved in two cases: all subnetworks that are not self‐synchronized and all subnetworks that are self‐synchronized. Moreover, an example is given to validate the effectiveness of the proposed controller.

Synchronization of time scales switched complex networks via impulsive couplings

“…Various kinds of schemes, including second smallest eigenvalues [10], Lyapunov functions [11][12][13], sliding mode technology [14], and Takagi-Sugeno fuzzy model [15], have been studied. Moreover, many control methods have been developed to facilitate synchronization of SCNs, such as adaptive control [16,17], feedback control [16,18], event-triggered control [19][20][21][22], pinning control [16,19,23,24], and impulsive control [12,15,25,26].…”

On reachable set problem for impulse switched singular systems with mixed delays

“…Usually, the impulse differential system is selected, which can better describe the changes of instantaneous state when the actual system is running, such as artificial intelligence and bioeconomics [4,5]. At present, there have been some theoretical studies on the ISS systems, such as stability, stabilization, synchronization, control problem [6][7][8]. However, the reachability of the ISS systems has not been totally studied.…”

Exponential bipartite synchronization of random signed networks with Markovian switching via impulsive control

“…So control strategies are needed to force them into synchronization. [25][26][27][28][29][30][31] As a relatively efficient and easily implemented strategy, impulsive control has the advantages of robustness and low cost. From the control time point of view, impulsive control does not need continuous input, and it only needs to be activated at discrete cases.…”

“…In fact, since many factors such as random disturbances and Markovian switching are considered simultaneously, it is difficult for signed networks to achieve bipartite synchronization by themselves. So control strategies are needed to force them into synchronization 25‐31 . As a relatively efficient and easily implemented strategy, impulsive control has the advantages of robustness and low cost.…”

“…From the control time point of view, impulsive control does not need continuous input, and it only needs to be activated at discrete cases. Due to these advantages of impulsive control, it has been widely used in many fields, such as space technologies and information science, and many interesting results have been obtained (see References 30‐32 and the references therein). Wang et al investigated the stability of complex‐valued stochastic delayed networks with Markovian switching and impulsive effects in Reference 30.…”