matlb solution dX/dt=AX(t)+B

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SAFA BOUDHRAA 2018-1-13

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编辑： SAFA BOUDHRAA 2018-1-14

morning, help me please, i am working i=on the resolution of the equation :dX/dt=AX(t)+B i have used ode45 but it gives wrong results . any suggests please thank you so much

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Answer 1

Star Strider 2018-1-13

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We need to see your code to determine what the problem is. The ODE solvers such as ode45, and for ‘stiff’ systems ode15s, should be able to solve it for linear or nonlinear ‘A’ matrices.

One way to solve it, if ‘A’ is a square, linear time-invariant (‘LTI’) matrix, is to use the matrix exponential expm (link) function.

Then:

x(t) = expm(A*t)*B

You will need to loop through values of ‘t’ to provide a matrix of solutions.

The Control System Toolbox also has several functions that will work.

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Answer 2

SAFA BOUDHRAA 2018-1-14

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编辑：SAFA BOUDHRAA 2018-1-14

function DY=resolution(t,y) A=[2*t 1 -3 sqrt(3) ;cos(t) 0 sqrt(2) -3 ;0 t -2 1; 4 sin(t) 0 t]; B=[0.5*t;1;0;0] dX=A*X+B ; end Q=zeros(4,1); Q(1,1)=12; [T,e] = ode45(@resolution,[0 2],Q); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%