On input function observers for generalized state-space systems
MOHAMMAD EL-TOHAMI, Victor Lovass-Nagy, David L. Powers · International Journal of Control · 1984
Linear control systems of the form E dx/dt = Ax;+ Bu, y = Cx + Du are considered, where E and A are not necessarily square matrices, and no assumption is made on the rank of the matrix pencil sE— A. The problem to be solved is this : find a system of the form Édz/dt = Âz + [Bcirc]ŷ, u = Ĉz + [Dcirc]ŷ where ŷ is some linear combination of y (the output of the original system) and its derivatives, and u is the input of the original system. For the solution of this problem, a method (based on the use of matrix generalized inverses) is developed that can be applied both to time-invariant and time-varying systems, A numerical procedure is elaborated for the time-invariant case that either yields a system Ê dz/dt = Âz + [Bcirc]ŷ, u =Ĉz + [Dcirc]ý (in which the coefficient matrices are of the smallest possible dimensions), or it shows that there is no such system. This procedure makes use of a recent paper of Wilkinson on singular systems of linear differential equations. In the special case where E =I, the procedure of this paper yields a minimal left inverse of the original system if a left inverse exists.