Given a Polytopic Linear Parameter Varying Descriptor System, this function computes the gains of a full order observer with unknown inputs [1]
[N,G1,L,H2,B1i]=lpvpuiobsv(E,A,B,C,R,alpha)
Continuos matrices of descriptor system. E singular. Where A=A(theta), B=B(theta), R= R(theta) and C=C. Theta is varying parameter.
For the stabilize the observer in a stable LMI region (see [1])
Gains matrices of the observer. This is obtained like N(j) where (j) is for the 1,2... j model of the polytopic observer
Auxiliar matrices for simulation, this can be obtained from qrrse transformation
Given a 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) This compute the observer gains for M dz/dt= Σmu(theta) [Nz(t) + G1u(t) + L(yo(t))] i=1 M xe(t)= Σmu(theta) [z(t) +H2(yo(t))] i=1 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).