A simple stability condition and decay rate estimation of time-delay systems

2012 ◽  
Author(s):  
Chien-Hua Lee ◽  
Cheng-Yi Chen
Keyword(s):  
Time Delay ◽  
Decay Rate ◽  
Stability Condition ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Rate Estimation ◽  
Estimation Of Time

Decay function estimation for linear time delay systems via the Lambert W function

2011 ◽  
Vol 18 (10) ◽  
pp. 1462-1473 ◽  
Author(s):  
Shiming Duan ◽  
Jun Ni ◽  
A Galip Ulsoy
Keyword(s):  
Time Delay ◽  
Decay Rate ◽  
Frequency Domain ◽  
Delay Systems ◽  
Lambert W Function ◽  
Time Delay Systems ◽  
Function Estimation ◽  
Decay Function ◽  
Optimal Decay ◽  
Optimal Decay Rate

The estimation of the decay function (i.e., [Formula: see text]; see equation (2)) for time delay systems has been a long-standing problem. Most existing methods focus on dominant decay rate (i.e., α) estimation, i.e., the estimation of the rightmost eigenvalue. Although some frequency domain approaches, such as bifurcation or finite dimensional approximation approaches are able to approximate the optimal decay rate computationally, the estimation of the factor, K, requires knowledge of the system trajectory over time and cannot be obtained from the frequency domain alone. The existing time domain approaches, such as matrix measure/norm or Lyapunov approaches, yield conservative estimates of decay rate. Furthermore, the factor K in the Lyapunov approaches is typically not optimized. A new Lambert W-function-based approach for estimation of the decay function for time delay systems is presented. This new approach is able to provide a closed-form solution for time delay systems in terms of an infinite series. Using this solution form, the optimal decay rate, α, and an estimate of the corresponding factor, K, can be obtained. Less conservative estimates of the decay function can lead to more accurate description of the exponential behavior of time delay systems, and more effective control design based on those results. The method is illustrated with several examples, and results compare favorably with existing methods for decay function estimation.

scholarly journals Robust H∞ Control For Uncertain Singular Neutral Time-Delay Systems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 217 ◽  
Author(s):  
Yuhong Huo ◽  
Jia-Bao Liu
Keyword(s):  
Time Delay ◽  
Stability Condition ◽  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Matrix Inequalities

The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ∞ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.

scholarly journals Exponential Estimates and Stabilization of Discrete-Time Singular Time-Delay Systems Subject to Actuator Saturation

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Jinxing Lin
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Decay Rate ◽  
Discrete Time ◽  
Actuator Saturation ◽  
Singular Systems ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Exponential Estimates ◽  
Singular Time

This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systems with time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskii function and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not only guarantees the regularity, causality, and exponential stability of the unforced system but also gives the corresponding estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under the proposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuator saturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initial conditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

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