This function compute the gains for a full order Proportiona-Integral observer with unknown inputs and useful for fault detection [1]
[N,G,L,Ti,H2,Phi]=piuiobsv(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
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) + Gu(t) + Ly(t)+Tide(t) xe= z(t) + H2y(t) dde/dt= Phi (y(t)-ye(t)) xe = stimated states y(t)=output ye(t)=stimated output de= stimated unknown input alpha put the observer in the stability LMI region
[1] Hamdi, H., Rodrigues, M., Mechmeche, C., & Theilliol, D. (2011). Fault Detection and Isolation for Linear Parameter Varying Descriptor Systems via Proportional Integral Observer. International Journal of Adaptive Control and Signal Processing, 2-16. doi:10.1002/acs