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MATLAB Script for Calculating Lower Bound using Small Gain Theorem, Assignments of Electrical and Electronics Engineering

Utah State University (USU)Electrical and Electronics Engineering

This matlab script calculates the lower bound value using the small gain theorem. The script defines several matrices p11, p12, p21, p22, i, and p0, and then calculates the inverse of i multiplied by p0 to find the matrix s0. The script also calculates the infinite norm of s0 and uses the small gain theorem to find the lower bound gamma_lower_bound.

Typology: Assignments

Pre 2010

Uploaded on 07/30/2009

koofers-user-3q0
koofers-user-3q0 🇺🇸

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===== start
% Problem 8.18
P11=nd2sys([1,-1],[1,2,1]);
P12=nd2sys([5,1],[1,2,1]);
P21=nd2sys([-1],[1,2,1]);
P22=nd2sys([1,-1],[1,2,1]);
% be careful about the I in S=1/(I+P0)!
% Although it looks like [1 0;0 1],
% it has totally different data structure!
I=sbs( abv(nd2sys(1,1),nd2sys(0,1)), abv(nd2sys(0,1),nd2sys(1,1)) );
P0=sbs( abv(P11,P21), abv(P12,P22) );
S0 = minv(madd(I,P0));
hinf_S0=hinfnorm(S0);
% then by small gain theorem, we know that
gamma_lower_bound=1/hinf_S0(2)
===== end

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===== start % Problem 8. P11=nd2sys([1,-1],[1,2,1]); P12=nd2sys([5,1],[1,2,1]); P21=nd2sys([-1],[1,2,1]); P22=nd2sys([1,-1],[1,2,1]); % be careful about the I in S=1/(I+P0)! % Although it looks like [1 0;0 1], % it has totally different data structure! I=sbs( abv(nd2sys(1,1),nd2sys(0,1)), abv(nd2sys(0,1),nd2sys(1,1)) ); P0=sbs( abv(P11,P21), abv(P12,P22) ); S0 = minv(madd(I,P0)); hinf_S0=hinfnorm(S0);

% then by small gain theorem, we know that gamma_lower_bound=1/hinf_S0(2) ===== end