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%% Balanced Realization of Stable System %% % Consider the following zero-pole-gain model, with near-canceling % pole-zero pairs: % Copyright 2015 The MathWorks, Inc. sys = zpk([-10 -20.01],[-5 -9.9 -20.1],1) %% % A state-space realization with balanced gramians is obtained by [sysb,g] = balreal(sys); %% % The diagonal entries of the joint gramian are g' %% % This indicates that the last two states of |sysb| are weakly coupled to % the input and output. You can then delete these states by sysr = modred(sysb,[2 3],'del'); %% % This yields the following first-order approximation of the original % system. zpk(sysr) %% % Compare the Bode responses of the original and reduced-order models. bodeplot(sys,sysr,'r--') %% % The plots shows that removing the second and third states does not have % much effect on system dynamics.