How to combine two ode systems?

Assume my colleague and I have developed two ode functions, respectively as:

• Function1: dx1=a1*x1+u1;
• Function2: dx2=a2*x2+u2;

For the integrated system, we know that u1=x2 and u2=x1 (i.e., feedback connection), but we don't want to explicitly rewrite a new function as:

• Function: dx=ax where a=[a1 1;1 a2].

So, is there a way to apply ode solvers on Function1 and Function2 respectively to get the integrated system's responses? Thanks in advance.

[Alka Nair]

Hi, Have you come across the function DSOLVE that solves a system of differential equation. I am not quite sure if I understand your question right, but please refer to the following link if you want to solve a system of differential equation:

http://in.mathworks.com/help/symbolic/solve-a-system-of-differential-equations.html

Answer 1

[Torsten]

You could solve the complete system (two differential and two algebraic equations):

dx1=a1*x1+u1;
dx2=a2*x2+u2;
0=u1-x2;
0=u2-x1;

Use the mass matrix option of the ODE integrators to add the algebraic equations.

Best wishes

Torsten.