An Uncertain Sandwich Impulsive Control System with Impulsive Time Windows

Abstract

In this paper, we formulate a new system, named the uncertain sandwich impulsive control system with impulsive time windows. The presented system shows that the linear entry matrix of the system is indeterminate. We first investigate the exponential stability of the considered system by linear matrix inequalities (LMIs) and inequalities techniques, then extend the considered system to a more general one and further study the stability of the general system. Finally, numerical simulations are delivered to demonstrate the effectiveness of the theoretical results.

Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value

“…The authors of [6] studied the stability and synchronization of complex-valued inertial neural networks using Caputo fractional derivatives, and particularly vividly demonstrated the dynamic synchronization phenomenon of complex-valued dynamic trajectories in both real and imaginary parts through numerical simulations (see, e.g., ). Chen et al proposed in [7] an uncertain sandwich control system with impulse time windows, which was well displayed in the computer simulations (Figures 2-5 in [7]). Reference [8] reported a new pulse control mode, which is a three-level pulse.…”

“…The series of papers in this Special Issue reflect the application of dynamic system theory in finance, neural networks, and other control systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For example, the authors of [1] studied the stability of PSS in hyperchaotic financial systems.…”

“…In addition, the authors of [6] used a direct analysis method to study the asymptotic stability and synchronization of a fractional order complex valued inertial neural network. Additionally, [7] reports that a new system was established, which is an uncertain sandwich pulse control system with a pulse time window. The calculation results indicate that the linear entry matrix of the system is uncertain.…”

“…The calculation results indicate that the linear entry matrix of the system is uncertain. In order to make this conclusion more general, the authors of [7] inserted a countable number of pulses during the T period and studied its exponential stability. Additionally, the authors of [8] successfully constructed a hyper-chaotic circuit system on the basis of the three-dimensional Chen system, using the smooth continuous nonlinear flux controlled reluctance model as the positive feedback term of the system, and realized the exponential stabilization of the memristor-based hyper-chaotic system by using the Lyapunov function and linear inequality matrix techniques.…”

“…On the other hand, the stability and synchronization control of dynamic systems are also among the main contents of cybernetics, and they are part of well-posed problems. Fifteen papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14] in this Special Issue deal with the stabilization and synchronization control of initial boundary value problems of partial differential equations or ordinary differential equations, and jointly complete the original work plan of this Special Issue. The papers in this Special Issue can be divided according to the following scheme considering their main purposes:…”