I want to solve some Lyapunov equations for stability analysis and find the solution of Ricatti equations based on Matrices. How can I do this in Matlab?
We can solve Riccati equation by "care" function .the manual of this function is:
if Ric(X ) = AT X + XA− XBBT X +Q = 0
[X,L,G,rr]=care(A,B,Q)
[X,L,G,rr]=care(A,B,Q,R,S,E)
if equation is discrete,we can solve this equation by "dare" function.
for solving lyapunov equation we can use "lyap" function:
X = lyap(A,Q)
X = lyap(A,B,C)
X = lyap(A,Q,[],E)
In order to solve Lyapunov or general linear matrix inequalities you need the LMI matlab toolbox. You can find other free software for LMI solution on the web, just look for lmi solvers on your internet search interface.
Lyapunov equation is a linear equation. Just write it in A x = b form and solve it. Riccati equation is a nonlinear equation, you can use policy iteration method to solve it. See the book by Prof. Lemon Zhou, Prof. Doyle, and Prof. Glover for it.
Article Robust and optimal control
The best tool is LMI toolbox or Robust Control toolbox. The lmiedit in Matlab makes it easy to write and solve your linear matrix inequalities.
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