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I am working on a research article

Local Stabilization of Time-Delay Nonlinear Discrete-Time Systems Using Takagi-Sugeno Models and Convex Optimization

written by Luís F. P. Silva, Valter J. S. Leite, Eugênio B. Castelan, and Michael Klug.

In this paper we get a state space like

dx = A*x + Ad * xd

here x are the states of system and xd are the delayed states.

I am getting confused that how do we plot the states of this system.

Cactus
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Ahmad Sheikh
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1 Answers1

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Possibilities:

  • The simplest thing to do is to plot the states of the system x against time as separate variables.
  • If the dimensionality is low (say <3), like in the example 4.1 at page 7, you can plot the phase space against time, as done in Figure 1, as a parametric curve. See also this entry of Wikipedia.
  • If the dimensionality is high, you may use Taken's embedding theorem to reduce the dimensionality. See in particular the "Simplified, slightly inaccurate version" for how to do it.
gg349
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  • Thank you for your help. actually i know about phase portraits... the thing creating trouble is that... if i have a differential equations like this... dx1 = 2*x + 3*xd ; dx2 = 0.5*x + 2*xd ; – Ahmad Sheikh Jan 06 '15 at 16:00
  • what about it? Clearly if you are dealing with delayed differential equations the problem has infinite dimensionality. This does not mean that you can't plot the state variable `x` at a certain time. And of course the evolution of the system will also depend on history. – gg349 Jan 06 '15 at 16:03
  • should i use dde23 command for this instead of ode45 in matlab..? – Ahmad Sheikh Jan 06 '15 at 16:19
  • if the problem is a delayed differential equation, yes. – gg349 Jan 06 '15 at 16:26