Further Results on the Achievable Delay Margin Using LTI Control

This technical note considers the delay margin problem of single-input single-output finite-dimensional linear time-invariant (FDLTI) plant with two or more real unstable poles by using LTI control. This research is the extension and further results of the previous result on plant with one real unstable pole. Explicit upper bound of the achievable delay margin is provided based on a frequency domain approach, and the bound can be transformed to the maximum value of a function of two variables.

[1]  Daniel E. Miller,et al.  Problem 8.3 Determining the least upper bound on the achievable delay margin , 2009 .

[2]  Daniel E. Miller,et al.  Stabilizing a SISO LTI Plant With Gain and Delay Margins as Large as Desired , 2014, IEEE Transactions on Automatic Control.

[3]  Silviu-Iulian Niculescu,et al.  Survey on Recent Results in the Stability and Control of Time-Delay Systems* , 2003 .

[4]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[5]  Wim Michiels,et al.  Continuous pole placement for delay equations , 2002, Autom..

[6]  Mathukumalli Vidyasagar,et al.  Control System Synthesis , 1985 .

[7]  A. Paor A modified Smith predictor and controller for unstable processes with time delay , 1985 .

[8]  S. Niculescu,et al.  Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach , 2007 .

[9]  Leonid Mirkin,et al.  Control Issues in Systems with Loop Delays , 2005, Handbook of Networked and Embedded Control Systems.

[10]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[11]  Daniel E. Miller,et al.  When is the Achievable Discrete-Time Delay Margin Nonzero? , 2011, IEEE Transactions on Automatic Control.

[12]  R. Devanathan A lower bound for limiting time delay for closed-loop stability of an arbitrary SISO plant , 1995, IEEE Trans. Autom. Control..

[13]  Jie Chen,et al.  Fundamental bounds on delay margin: When is a delay system stabilizable? , 2014, Proceedings of the 33rd Chinese Control Conference.

[14]  Daniel E. Miller,et al.  On the Achievable Delay Margin Using LTI Control for Unstable Plants , 2007, IEEE Transactions on Automatic Control.

[15]  Rifat Sipahi,et al.  Delay-margin design for the general class of single-delay retarded-type LTI systems , 2014 .

[16]  Lihua Xie,et al.  Input delay margin for consensusability of multi-agent systems , 2013, Autom..

[17]  Daniel E. Miller,et al.  Stabilization in the presence of an uncertain arbitrarily large delay , 2005, IEEE Transactions on Automatic Control.