MATLAB: State space modeling of LTI

Question

I have a LTI system is given in the attached picture. For which I have A=[0 1;1 2] B=[1;1], C=[3,4], D=0.1 and L=[0 1]. I need to find z(t) over an interval [0,20] and initial condition is assumed as x0=[1;-1] with an input w=0.5sin(2pi)t and v=t, how can I make a code for this??

Answer 1

Such LTI system can be solved using lsim

C=[3,4]; 
D=0.1;
L=[0 1];
sys = ss(A,B,C,D);
t = linspace(0,20,1000)';
x0 = [1; -1];
[t,x] = ode45(@odeFun, t, x0);
v = t;
y = C*x' + D*v';
z = L*x';
plot(t,z)
function dxdt = odeFun(t, x)
    A=[0 1;1 2];
    B=[1;1];
    w = 0.5*sin(2*pi*t);
    
    dxdt = A*x+B*w;
end

However, the system is unstable and the output diverges to infinity.