www.gusucode.com > control 案例程序 matlab源码代码 > control/PlotSectorIndexVersusFrequencyExample.m

    %% Plot Sector Index Versus Frequency
% Plot the sector index to visualize the frequencies at which the I/O
% trajectories of $G\left( s \right) = \left( {s + 2} \right)/\left( {s +
% 1} \right)$ lie within the sector defined by: 
%
% $$ S = \left\{ {\left( {y,u} \right):0.1{u^2} < uy < 10{u^2}} \right\}. $$
%%
% In U/Y space, this sector is the shaded region of the following diagram.
%%
% 
% <<../sector_diagram1.png>>
% 
%%
% The Q matrix for this sector is given by:
a = 0.1;  
b = 10; 
Q = [1 -(a+b)/2 ; -(a+b)/2 a*b];
%%
% A trajectory $y\left( t \right) = G{\kern 1pt} u\left( t \right)$ lies
% within the sector _S_ when for all _T_ > 0,
%
% $$0.1\int_0^T {u{{\left( t \right)}^2} < } \;\;\int_0^T {u\left( t
% \right)y\left( t \right)dt < } \;\;10\int_0^T {u{{\left( t \right)}^2}dt}
% .$$
%%
% In the frequency domain, this same condition can be expressed as:
% 
% $${\left( {\begin{array}{*{20}{c}} {G\left( {j\omega } \right)}\\ 1
% \end{array}} \right)^H}Q\left( {\begin{array}{*{20}{c}} {G\left( {j\omega
% } \right)}\\ 1 \end{array}} \right) < 0.$$ 
%
%%
% To check whether |G| satisfies or violates this condition at any
% frequency, plot the sector index for |H = [G;1]|.
G = tf([1 2],[1 1]); 
sectorplot([G;1],Q)
%%
% The plot shows that the sector index is less than 1 at all frequencies.
% Therefore, the trajectories of G(s) fit within in the specified sector Q
% at all frequencies.