CODEWITHSUNDEEP
nonlinear-functionstimedelaystate-space
Ahmad Sheikh
Ahmad Sheikh

Reputation: 21

how to plot states of a state space having time delayed states in matlab?

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.

Upvotes: 2

Views: 651

Answers (1)

gg349
gg349

Reputation: 22681

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.

Upvotes: 1

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