MATLAB: Differential equation x˙=−Lx

equationx˙=−lx

how can I write the equation below in matlab? preferably discretized.
x˙=−Lx
L is a 7*7 matrix and x is a 7*2 matrix.

Best Answer

I assume this is a differential equation.
Derivation:
x’ = -L*x              —> Laplace transform —> 
s*X = -L*X + x0
(sI* + L)*X = x0
X = (s*I + L)^-1*x0   Note: ‘^-1’ denotes the inverse
x = expm(-L)*x0       <— SOLUTION  x0 are the initial conditions
In practical terms:
L = randi(99, 7);                                       % Create Matrix
x0 = randi(9, 7, 2);                                    % Initial Conditions
x = expm(-L)*x0;                                        % Solved System
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