solving state variable equation in matlab

hello i am trying this eqution :

dx/dt=A*x+B*u

y=C*x

while A is matrix 4X4,B is matrix 4X1,C is matrix 1X4,and u is constant , how do i find X ? if X should be matrix of 4X1 , and how do i draw graph of x ?

Answer 1

[M]

WHat do you want to do exactly ?

If you want to simulate your system with a given input, you can use specific function, such as step, impulse etc...

You can also solve your ODE system with the matlab ode45 solver.

Answer 2

[tomer polsky]

ye i tried to use ode system but i cant understand how to write it.could you write me example for second order code ?

Answer 3

[M]

Take a look at this :

https://fr.mathworks.com/matlabcentral/answers/146782-solve-state-space-equation-by-ode45

or this

https://fr.mathworks.com/matlabcentral/answers/142123-using-ode45-to-solve-a-state-space-system

Answer 4

[Star Strider]

Your integrated differential equation is the matrix exponential, given by the expm function (in both base MATLAB and the Symbolic Math Toolbox).

The integration of your system is:

dx/dt = A*x + B*u                                       % Time-Domain Differential Equation
y = C*x

sX = A*X + B*U                                          % Laplace Transformed System
Y = C*X

sX - A*X = B*U                                          % Rearrange
Y = C*X

(s*I -A)*X = B*U                                        % Combine Terms, ‘I’ Is The Identity (‘eye’) Matrix
Y = C*X

X = inv(s*I - A)*B*U                                    % Solve For ‘X’ (Do Not Use ‘inv’), Illustration Only Here
Y = C*X

Y = C*(inv(s*I - A)*B*U)                                % Substitute

y(t) = C*expm(A*t)*B*u(t)                               % Inverse Laplace Transform To Get Solved Differential Equation

This is straightforward to calculate in a loop.