Given a Polytopic Linear Parameter Varying Descriptor System, this function computes a bank of observers in a Generalized observer scheme (GOS) by a full order observer with unknown inputs [1,2]
[N,G1,L,H2,Bo1]=lpvgosbank(E,A,B,C,R,alpha,flag)
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])
flag='s' for sensor faults and 'a' for actuator faults. By default is programed for sensor faults
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 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) This compute the observer gains 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 Example Gos for actuator faults (AFD) u inputs (in) outputs __________ -------| LPV model|------------- ------ |__________|------------ __________ in2-------| LPV Obsv1------------- in2------|__________|------------- inm------ __________ in1-------| LPV obsv2|------------- in3-------|__________|------------- inm-------- __________ in1 ----| LPV obsvm |------------- in2 -------|__________|------------- in(m-1)----
[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).