From: Pascal Gahinet Newsgroups: comp.soft-sys.matlab,comp.software-eng,sci.math,sci.engr.control Subject: Re: a pencil based approach for solving the Riccati equation Date: Thu, 26 Mar 1998 13:15:12 -0500 Dear Bogdan The DARE command in the versions 4.0 and above of the Control System Toolbox solve discrete-time Riccati equations using precisely this method. Included is the help for DARE: - pascal DARE Solve discrete-time algebraic Riccati equations. [X,L,G,RR] = DARE(A,B,Q,R,S,E) computes the unique symmetric stabilizing solution X of the discrete-time algebraic Riccati equation -1 E'XE = A'XA - (A'XB + S)(B'XB + R) (A'XB + S)' + Q or, equivalently (if R is nonsingular) -1 -1 -1 E'XE = F'XF - F'XB(B'XB + R) B'XF + Q - SR S' with F:=A-BR S'. When omitted, R,S and E are set to the default values R=I, S=0, and E=I. Additional optional outputs include the gain matrix -1 G = (B'XB + R) (B'XA + S'), the vector L of closed-loop eigenvalues (i.e., EIG(A-B*G,E)), and the Frobenius norm RR of the relative residual matrix. See also CARE. Bogdan.Marinescu@der.edfgdf.fr wrote: > Hello World! > > I have to solve a Riccati equation associated to a > discrete-time control problem in which the state matrix > A is singular. The approach I used is based on the > computing of the invariant sub-spaces of the associated > matrix pencil (see, e.g., P. Van Dooren (1981) "Generalized > eigenvalue approach for solving the Riccati equation", > SIAM J. on Sci. St. Comp. 2, pp. 121-135 or V. Ionescu > and M. Weiss (1992) "On computing the stabilising solution > to the discrete-time Riccati equation", Linear algebra > and its applications, 174:229-238. > I will be grateful if somebody could indicate me if there > is any professional C software to solve this problem. > Also, I'm not sure if there is any toolbox (Mathworks or not) > containing an m.(MATLAB) file which solves this problem. > Please let me know if you have some information about this > kind of software. > Thanking you in advance, > > Sincerely yours, > > Bogdan Marinescu > > -----== Posted via Deja News, The Leader in Internet Discussion ==----- > http://www.dejanews.com/ Now offering spam-free web-based newsreading