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Diffstat (limited to 'modules/cacsd/macros/linf.sci')
-rwxr-xr-x | modules/cacsd/macros/linf.sci | 68 |
1 files changed, 68 insertions, 0 deletions
diff --git a/modules/cacsd/macros/linf.sci b/modules/cacsd/macros/linf.sci new file mode 100755 index 000000000..7cb6ef315 --- /dev/null +++ b/modules/cacsd/macros/linf.sci @@ -0,0 +1,68 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) INRIA - +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +function [n]=linf(g,eps,tol) + //linf(g,[eps],[tol]) L_infinity norm + // n=sup [sigmax(g(jw)] (sigmax largest singular value). + // w + //-- g is a syslin system. + //-- eps is error tolerance on n. + //-- tol threshold for imaginary axis poles. + // See also: h_norm + //! + if type(g)==1,if norm(g)==0,n=0,return,end,end, + + if and(typeof(g)<>["rational","state-space"]) then + error(msprintf(gettext("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n"),"linf",1)) + end + if g.dt<>"c"&g.dt<>[] then + error(msprintf(gettext("%s: Wrong value for input argument #%d: Continuous time system expected.\n"),"linf",1)) + end + g.dt="c" + if typeof(g)=="rational" then g=tf2ss(g),end + + [lhs,rhs]=argn(0), + select rhs, + case 1 then eps=1e-7,tol=1000*%eps, + case 2 then tol=1000*%eps, + end, + [a,b,c,d]=g(2:5),[t,t]=size(a), + p=ctr_gram(g),q=obs_gram(g); + //Algorithm: + //---------- + //1. min , max. + //---------------------------------- + [slp,slm]=dtsi(g), + if slp==0 then pp=0,qq=0,tp=1, + pm=p,qm=q,tm=t, + else + if slm==0 then pm=0,qm=0,tm=1, + pp=p,qq=q,tp=t, + else + [tp,tp]=size(slp(2)),[tm,tm]=size(slm(2)), + pp=ctr_gram(slp),qq=obs_gram(slp), + pm=ctr_gram(slm),qm=obs_gram(slm), + end, + end, + hsvp=sqrt(spec(pp*qq)),hsvp=gsort(real(hsvp)), + hsvm=sqrt(spec(pm*qm)),hsvm=gsort(real(hsvm)), + gl=max([norm(d),hsvp(tp),hsvm(tm)]), + gu=norm(d)+2*(sum(hsvp)+sum(hsvm)), + //2. binary search + //---------------------- + while gu-gl>2*eps*gl, + x=(gl+gu)/2, + r=d'*d-(x*x)*eye(),s=d*d'-(x*x)*eye(), + mx=[a-b/r*d'*c, -x*b/r*b'; .. + x*c'/s*c, -a'+c'*d/r*b'], + mp=abs(real(spec(mx))),mp=min(mp), + if mp>tol then gu=x, else gl=x, end, + end; + n=(gu+gl)/2 +endfunction |