The Framework for Linear Periodic Time‐Delay Systems Based on Semi‐Discretization: Stability Analysis and Control

Abstract

Stability analysis and control for linear periodic time-delay systems are investigated in this paper. In this framework, a semi-discretization method is used to develop a mapping of the system response in a finite-dimensional state space. With the mapping, the stability region and stability boundary can be identified by comparing the maximum absolute value of its eigenvalues to 1. More importantly, an efficient stability criterion is presented for periodic neutral systems. In addition, minimization of the maximum absolute value of the mapping's eigenvalues leads to optimal control gains. The tracking control problem is also discussed. Two numerical examples are given to illustrate the effectiveness of the proposed method.

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

“…with the boundary conditions given by (4). The parameters A z (t), B z (t) and C z (t) are defined by (8),…”

“…Recently, control and optimization of time-delay systems have been of interest to many researchers [1][2][3][4][5]. The presence of delay makes the analysis and control of such systems much more complicated.…”

Control for Time‐Varying Delay Systems by Integrating Semi‐Discretization and Hysteresis‐Based Switching

“…Moreover, semi‐discretization is proposed to find an optimal controller for an arbitrary delay value. It has been demonstrated by our previous works that semi‐discretization is able to find optimal controllers through solving an optimization problem. In , we also proved that semi‐discretization based approach can reduce conservatism compared with other control design methods.…”

“…Then stacking the mappings over multiple time steps yields a very accurate transition matrix, using which stability analysis and control designs can be conducted conveniently. Semi‐discretization has been successfully applied to derive the necessary and sufficient stability conditions for second order linear time‐invariant TDSs , linear periodic TDSs , and neutral periodic TDSs . Additionally, performance analysis and control design were investigated using the semi‐discretization method .…”

“…Semi‐discretization has been successfully applied to derive the necessary and sufficient stability conditions for second order linear time‐invariant TDSs , linear periodic TDSs , and neutral periodic TDSs . Additionally, performance analysis and control design were investigated using the semi‐discretization method . It is worth noting that the semi‐discretized TDS has the same stability properties with the original TDS, if the semi‐discretization level is sufficiently fine .…”