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# hinfnorm

% Computes the

## SYNOPSIS

function [g, gmin, gmax] = hinfnorm (sys, tol, gmin, gmax, ptol)

## DESCRIPTION

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{g}, @var{gmin}, @var{gmax}] =} hinfnorm (@var{sys}, @var{tol}, @var{gmin}, @var{gmax}, @var{ptol})
% Computes the
% @iftex
% @tex
% ${ \cal H }_\infty$
% @end tex
% @end iftex
% @ifinfo
% H-infinity
% @end ifinfo
% norm of a system data structure.
%
% @strong{Inputs}
% @table @var
% @item sys
% system data structure
% @item tol
% @iftex
% @tex
% ${ \cal H }_\infty$
% @end tex
% @end iftex
% @ifinfo
% H-infinity
% @end ifinfo
% norm search tolerance (default: 0.001)
% @item gmin
% minimum value for norm search (default: 1e-9)
% @item gmax
% maximum value for norm search (default: 1e+9)
% @item ptol
% pole tolerance:
% @itemize @bullet
% @item if sys is continuous, poles with
% @iftex
% @tex
% $\vert {\rm real}(pole) \vert < ptol \Vert H \Vert$
% @end tex
% @end iftex
% @ifinfo
% @math{ |real(pole))| < ptol*|H| }
% @end ifinfo
% (@var{H} is appropriate Hamiltonian)
% are considered to be on the imaginary axis.
%
% @item if sys is discrete, poles with
% @iftex
% @tex
% $\vert { \rm pole } - 1 \vert < ptol \Vert [ s_1 s_2 ] \Vert$
% @end tex
% @end iftex
% @ifinfo
% @math{|abs(pole)-1| < ptol*|[s1,s2]|}
% @end ifinfo
% (appropriate symplectic pencil)
% are considered to be on the unit circle.
%
% @item Default value: 1e-9
% @end itemize
% @end table
%
% @strong{Outputs}
% @table @var
% @item g
% Computed gain, within @var{tol} of actual gain.  @var{g} is returned as Inf
% if the system is unstable.
% @item gmin
% @itemx gmax
% Actual system gain lies in the interval [@var{gmin}, @var{gmax}].
% @end table
%
% References:
% Doyle, Glover, Khargonekar, Francis, @cite{State-space solutions to standard}
% @iftex
% @tex
% ${ \cal H }_2$ @cite{and} ${ \cal H }_\infty$
% @end tex
% @end iftex
% @ifinfo
% @cite{H-2 and H-infinity}
% @end ifinfo
% @cite{control problems}, @acronym{IEEE} @acronym{TAC} August 1989;
% Iglesias and Glover, @cite{State-Space approach to discrete-time}
% @iftex
% @tex
% ${ \cal H }_\infty$
% @end tex
% @end iftex
% @ifinfo
% @cite{H-infinity}
% @end ifinfo
% @cite{control}, Int. J. Control, vol 54, no. 5, 1991;
% Zhou, Doyle, Glover, @cite{Robust and Optimal Control}, Prentice-Hall, 1996.
% @end deftypefn

## CROSS-REFERENCE INFORMATION

This function calls:
• is_digital % Return nonzero if system is digital.
• is_stable % Returns 1 if the matrix @var{a} or the system @var{sys}
• sys2ss % Extract state space representation from system data structure.
• sysdimensions % return the number of states, inputs, and/or outputs in the system
• sysupdate % Update the internal representation of a system.
This function is called by:
• dgkfdemo % Octave Controls toolbox demo:

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