Relative controllability of multiagent systems with pairwise different delays in states

In this manuscript, relative controllability of leader–follower multiagent systems with pairwise different delays in states and fixed interaction topology is considered. The interaction topology of the group of agents is modeled by a directed graph. The agents with unidirectional information flows are selected as leaders, and the others are followers. Dynamics of each follower obeys a generic time-invariant delay differential equation, and the delays of agents, which satisfy a specified condition, are different one another because of the degeneration or burn-in of sensors. With a neighbor-based protocol steering, the dynamics of followers become a compact form with multiple delays. Solution of the multidelayed system without pairwise matrices permutation is obtained by improving the method in the references, and relative controllability is established via Gramian criterion. Further rank criterion of a single delay system is dealt with. Simulation illustrates the theoretical deduction.

Asymptotic Analysis of Spectrum and Stability for One Class of Singularly Perturbed Neutral-Type Time-Delay Systems

In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically into two much simpler parameter-free subsystems, the slow and fast ones. Using this decomposition, an asymptotic analysis of the spectrum of the considered system is carried out. Based on this spectrum analysis, parameter-free conditions guaranteeing the exponential stability of the original system for all sufficiently small values of the parameter are derived. Illustrative examples are presented.

History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems

We study a new frictionless quasistatic contact problem for viscoelastic materials, in which contact conditions are described by the fractional Clarke generalized gradient of nonconvex and nonsmooth functions and a time-delay system. In addition, our constitutive relation is modeled using the fractional Kelvin–Voigt law with long memory. The existence of mild solutions for new history-dependent fractional differential hemivariational inequalities with a time-delay system are obtained by the Rothe method, properties of the Clarke generalized gradient, and a fixed-point theorem.

Linear time-delay circuit and stabilizing controller

This paper is concerned with a linear time-delay circuit and its feedback control. We use electronic components such as resistors and capacitors to realize a linear time-delay system. The time-delays are generated by operational amplifiers and single-chip microcomputers. Based on the actual data measured by the oscilloscope, the parameters of the system are estimated using the least square method. Then a comparison study between the waveform image measured by the oscilloscope and the numerical simulation obtained by MATLAB verifies the effectiveness of the parameters estimations of the circuit system. Furthermore, the circuit system is unstable with a large time-delay, a feedback controller is designed to stabilize the circuit system using the optimization method in the literature. Finally, the experimental results in the linear time-delay circuit show the effectiveness of the optimization method.

Robust optimal control of a nonlinear impulsive time-delay system for 1,3-PD fed-batch culture

In this paper, taking the feeding process as a form of impulsive and considering the time-delay in fermentation process. A robust model with the time-delay system as the control variable and the time-delay system as the constraint is established. In order to solve this optimal control problem, we have propose an particle swarm optimization method to solve problem. Numerical results show that 1,3-PD yield at the terminal time increases compared with the experimental result.