Is it possible to implement an array as a variable inside a state space matrix?

Hello all, I am new to control systems and state space matrix, I am working a creating a script for modeling the cardiovascular system. I have the statespace matrix for the model however the first varabile of the matrix C_dot/C(t) is a function that varies with time. I have the array for this variable but I am having trouble with how it is implemnted within the state matrix.

HR=60; %Heart Rate BPM

E_max=2; %mmHg/ml

E_min=.06; %mmHg/ml

t=0:.01:3;

t_c=60/HR; %Cardiac Cycle

T_max=.2+.15*t_c;

t_n=t./T_max;

%Normalized Elastance

A=((t_n./.7).^1.9)./(1+((t_n./.7).^1.9));

B=1./(1+((t_n./1.17).^21.9));

E_n=1.55.*A.*B;

%Elastance

E=(E_max-E_min).*E_n+E_min;

plot(t,E)

xlabel('Time(s)')

ylabel('mmHg/ml')

xlim([0 .8])

title('Graph of Elastance againt Time')

figure ()

%Compliance

C=1./E;

plot(t,C)

xlabel('Time(s)')

ylabel('ml/mmHg')

title('Graph of Compliance againt Time')

xlim([0 .8])

figure()

%Derivative of Compliance

C_dot=diff(C);

C_dot1=[C_dot,1];

C_both=-C_dot1./C;

plot(t,C_both);

xlabel('Time(s)')

xlim([0 .8])

ylabel('(-dC/dt)/C(t)')

title('Graph of -C_dot/C(t) againt Time')

%Constant Values of 5th order

Rs=1.0000; %Systemic Vascular Resistance(SVR)

Rm=0.0050; %Mitral Valve Resistance

Ra=0.0010; %Aortic Valve Resistance

Rc=0.0398; %Characteristic Resistance

Cr=4.4000; %Left Atrial Compliance

Cs=1.3300; %Systemic Compliance

Ca=0.0800; %Aortic Compliance

Ls=0.0005; %Inertance of blood in Aorta

%Matrix

%X1(t) LVP(t) Left Ventricular 7.6 mmHg

%X2(t) LAP(t) Left Atrial Pressure 7.6 mmHg

%X3(t) AP(t) Arterial Pressure 67 mmHg

%X4(t) AoP(t) Aortic Pressure 80 mmHg

%X5(t) Qao(t) Aortic Flow 0 ml/s

% 1's are in the place of variables that are arrays

A_matrix=[1 0 0 0 0;

0 -1/Rs*Cs 1/Rs*Cs 0 0 ;

0 1/Rs*Cs -1/Rs*Cs 0 1/Cs ;

0 0 0 0 -1/Ca ;

0 0 -1/Ls 1/Ls -Rc/Cs];

Answer 1

[Star Strider]

You would have to integrate your model using one of the numerical integrators such as ode45. It is definitely possible to use your vector of values for it. See the documentation section on ODE with Time-Dependent Terms for details.