This function generates wieighting function for a Polytopic Linear Parameter Varying Descriptor System of four vertices
[mus]=lpvweig4(Theta,vert)
Is the vector of measured parameter. This could be an scalar or a vector. E.g. Theta=[Theta1 Theta2]= [0.04 0.1]
Are the maximun and minimun limits of the parameters. E.g. vert=[minTheta1 maxTheta1; minTheta2 maxTheta2]=[-0.05 0.05; -0.1 0.1]. Usuallly it is constant.
It is the vector of weightings function. mus=[mu1 mu2 mu3 mu4 sum(mu)]. sum(mu) =1 for all time
Given a polytopic LPV Descriptor system in the form M dxEdt= Σmu(theta)[A(theta) x(t) + B(theta) u(t) +R(theta) d (t)] i=1 y =C x(t) + D u(t) Where theta is the parameter varying and it is bounde by four vertices. The function builds the weighting function Σmu(theta) given the vertices and the measured parameters theta.
// parameter varying theta1=[-0.05 0.05]; //[ ] theta2=[-0.1 0.1 ]; vert=[theta1; theta2] // vertices of the polytope // for one vector Thetas=[0.04 -0.1] [musa]=lpvweig4(Thetas,vert) // given a vector of measured parameters // this it is very useful for simulation Theta1=prbs_a(length(0:101),10)/20; Theta2=prbs_a(length(0:101),10)/10; Thetas=[Theta1; Theta2]; [musa]=lpvweig4(Thetas,vert) // for a column vector Theta1=Theta1'; Theta2=Theta2'; Thetas=[Theta1 Theta2]; [musa]=lpvweig4(Thetas,vert) // plotting figure(1); clf(); t=1:size(musa,1); subplot(211) plot(t,Thetas) legend('Parameter varying') subplot(212) plot(t,musa) legend('Weighting functions') | ![]() | ![]() |
[1] M., Hamdi., Rodrigues, M., Mechmeche, C., Theilliol, D., Braiek, N. B., & Tunisie, E. P. D. (2009). State Estimation for Polytopic LPV Descriptor Systems : Application to Fault Diagnosis. Convergence (pp. 438-443).