Which lyapunov equation to use for my model?

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Yasmin Tamimi 2012-11-13

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https://ww2.mathworks.cn/matlabcentral/answers/53576-which-lyapunov-equation-to-use-for-my-model

Hey all,

I have a dynamical system and modeled it using System Identification Toolbox and ended up with this format:

State-space model: x(t+Ts) = A x(t) + B u(t) + K e(t) y(t) = C x(t) + D u(t) + e(t)

So under dlyap we have three different types: 1] X = dlyap(A,Q) solves the discrete-time Lyapunov equation. 2] X = dlyap(A,B,C) solves the Sylvester equation AXBT − X + C = 0. 3] X = dlyap(A,Q,[],E) solves the generalized discrete-time Lyapunov equation AXAT − EXET + Q= 0.

So, which of the shall be used and why?

I have seen some examples for solving with dlyap and in each one they are solving in a different way and sometime they are transposing matrix A!! http://www.ece.rutgers.edu/~gajic/psfiles/LinearLyapunov.pdf http://www.stanford.edu/class/ee363/hw/hw5sol.pdf

Any help is really appreciated!