This function generates wieighting function for a Polytopic Linear Parameter Varying Descriptor System of two vertices
[mus]=lpvweig2(theta)
Is the measured parameter varying. This could be an scalar or a vector.
It is the vector of weightings function. mus=[mu1 mu2 sum(mu)] ^T. 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 two 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=lpvweig2(theta) // given a vector of measured parameters // this it is very useful for simulation theta=rand (1:40); mus=lpvweig2(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] Theilliol, D., & Aberkane, S. (n.d.). Design of LPV observers with unmeasurable gain scheduling variable under sensor faults. IFAC World Congress 2011.
[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).