Systems with Single Delay

  • Keqin Gu
  • Vladimir L. Kharitonov
  • Jie Chen
Part of the Control Engineering book series (CONTRENGIN)


In this chapter we will explore the time domain approaches of stability analysis. An advantage of time domain methods is the ease of handling nonlinearity and time-varying uncertainties. However, in order to illustrate the basic ideas, in this chapter we will concentrate on the stability problem of linear time-invariant systems with single delay
$$\dot x\left( t \right) = {A_0}x\left( t \right) + {A_1}x\left( {t - r} \right)$$
where Ao and Al are given n x n real matrices. The usual initial condition is in the form of
$${x_0} = \phi$$
We will defer the discussions on the uncertainties and systems with multiple delays as well as distributed delays to later chapters.


Stability Criterion Linear Matrix Inequality Model Transformation Additional Pole Real Symmetric Matrix 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Keqin Gu
    • 1
  • Vladimir L. Kharitonov
    • 2
  • Jie Chen
    • 3
  1. 1.Department of Mechanical and Industrial EngineeringSouthern Illinois University at EdwardsvilleEdwardsvilleUSA
  2. 2.Department of Automatic ControlCINVESTAV-IPNMexico, D.F.Mexico
  3. 3.Department of Electrical EngineeringUniversity of California at RiversideRiversideUSA

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