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+// Example 15.9

+// Calculating the Zero-State Response

+s=%s;

+t=0:0.001:5;

+// From Transfer function Matrix equation i.e.

+//P(s)*H(s)=C*adj[s*I-A]*B+P(s)*[D+s*E]

+// Substituting various Matrices into the above equations we get

+P_s= (s+3)*(s+5)

+W=[6,10;0,-2]*[s,-5;3,s+8]*[-8,0;3,1]+(P_s)*[0,0;2,0];

+H_s=W/P_s;

+

+//To obtain the Zero-state outputs produced by x1(t)=u(t) and x2(t)=0

+X_s=[1/s;0]; // Laplace transform of input matrix

+Y_s=H_s*X_s;

+// Writing down two elements of Y_s

+Y_1=-18/(s*(s+3));

+// taking inverse laplace of Y_1

+y1= -6+6*exp(-3*t);

+Y_2=(2*s^2+10*s+30)/(s*(s+3)*(s+5));

+// taking inverse laplace of Y_2

+y2=2-3*exp(-3*t)+exp(-5*t);

+plot(t,y1,'-r',t,y2,'-g')

+xlabel('t')

+ylabel('y(t)')

+title('Signal Waveform')

+h1=legend(['y1';'y2']);