Hello, everyone,
I try to find a phase portrait of first order systems of the forme X'=AX+BU, and so, for trying to explain the effect of the choice of the initial conditions to the convergence, any suggestions ??
With thanks !!
Quick answer: YES
Regardless the system is linear or non-linear the phase space analysis is always valid close to the equilibrium points (X points satisfying AX+BU=0), hence the overall structure is qualitatively valid.
Siempre que el sistema estudiado sea autónomo, podrás hacer el análisis de su retrato fase, en particular X'=AX+BU.
However, there exist non-linear autonomous systems without equilibrium points and the phase portrait analisys is not applicable until now... There isn't problem with linear autonomous control systems in the form x'=Ax+Bu, the phase portrait analisys is applicable without a problem, as long as the control u doesn't cause troubles...
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