Stability of Time-Delay Systems pp 147-195 | Cite as
Systems with Single Delay
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Abstract
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
where Ao and Al are given n x n real matrices. The usual initial condition is in the form of
We will defer the discussions on the uncertainties and systems with multiple delays as well as distributed delays to later chapters.
$$\dot x\left( t \right) = {A_0}x\left( t \right) + {A_1}x\left( {t - r} \right)$$
(5.1)
$${x_0} = \phi$$
(5.2)
Keywords
Stability Criterion Linear Matrix Inequality Model Transformation Additional Pole Real Symmetric Matrix
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Science+Business Media New York 2003