This function compute the gains for a full order observer with unknown inputs [1]
[N,G1,L,H2,B1]=puiobsv(E,A,B,C,R,alpha)
Continuos matrices of descriptor system. E singular
For the stabilize the observer in a stable LMI region (see [1])
Gains matrices of the observer
Auxiliar matrices for simulation, this can be obtained from qrrse transformation
Given a Descriptor system in the form dxEdt=A x(t) + B u(t) +R d (t) y =C x(t) + D u(t) This compute the observer gains for dz/dt= Nz(t) + G1u(t) + L(yo(t)) xe(t)= z(t) +H2(yo(t)) where yo(t) results from QR r.s.e transformation yo(t)=[-B1u(t); y(t)]; y(t)= C x(t) alpha put the observer in the stability LMI region
[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).