This function generates wieighting function for a Polytopic Linear Parameter Varying Descriptor System of three vertices
[mus]=lpvweig3(theta)
Is the measured parameter varying. This could be an scalar or a vector.
It is the vector of weightings function. mus=[mu1 mu2 mu3 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 three vertices. This funtion is very usefull when the parameter varyin is an state of the systems (see [1]). The function builds the weighting function Σmu(theta) given the vertices and the measured parameters theta.
// parameter varying theta=0.5; mus=lpvweig3(theta) // given a vector of measured parameters // this it is very useful for simulation theta=rand (1:40); mus=lpvweig3(theta) // plotting figure(1); clf(); t=1:size(mus,2); subplot(211) plot(t,theta) legend('Parameter varying') subplot(212) plot(t,mus) legend('Weighting functions') | ![]() | ![]() |
[1] Habib, H., Rodrigues, M., Mechmeche, C., & Benhadj, N. (2010). Robust H ∞ Fault Diagnosis for Multi-Model Descriptor Systems : A. Control.
[2] 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).