Re: Lyapunov Equation

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg729] Re: Lyapunov Equation*From*: rubin at msu.edu (Paul A. Rubin)*Date*: 11 Apr 1995 21:28:58 GMT*Organization*: Michigan State University

In article <3md5uo$9fp at news0.cybernetics.net>, ggb at bigdog.engr.arizona.edu (Gene Bergmeier) wrote: ->Pardon the silly question, but my roommate and I are just beginning to ->use Mathematica. We are attempting to solve the Lyapunov equation (from ->nonlinear controls). The equation is -> -> PA+Trans(A)P=-Q where -> -> Q=I -> P is symmetric -> and A is general. -> ->We have tried the following procedure. Set Q equal to a 2D identity ->matrix, P as a matrix of p11, p12 and p22 and A as a matrix of known ->coefficients. Then we stated the Lyapunov eq and asked Mathematica to ->solve it for p11, p12 and p22. -> ->Any thoughts or suggestions? -> ->Thanks for the help. -> ->Gene :) -> ->--------------------------------------------------------------------- ->Gene Bergmeier ->ggb at bigdog.engr.arizona.edu ->--------------------------------------------------------------------- That works (assuming that you remember to use Dot (.) for the matrix multiplications and Equal (==) for the equation): In[1]:= p = {{p11, p12}, {p12, p22}}; In[2]:= q = IdentityMatrix[ 2 ]; In[3]:= a = Table[ 2 Random[] - .5, {i, 2}, {j, 2} ] Out[3]= {{-0.243847, 1.20228}, {0.504195, -0.312064}} In[4]:= p0 = Flatten[ p /. Solve[ p . a + Transpose[ a ] . p == q, Union[ Flatten[ p ] ] ], 1 ] Out[4]= {{-0.302853, 0.845209}, {0.845209, 1.65407}} In[5]:= p0 . a + Transpose[ a ] . p0 (* checking the answer *) Out[5]= {{1., 0.}, {0., 1.}} Paul ************************************************************************** * Paul A. Rubin Phone: (517) 432-3509 * * Department of Management Fax: (517) 432-1111 * * Eli Broad Graduate School of Management Net: RUBIN at MSU.EDU * * Michigan State University * * East Lansing, MI 48824-1122 (USA) * ************************************************************************** Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. J. W. v. GOETHE