On the control of linear systems having internal variations. (Q1421433)

The authors study the control of a collection of implicit systems. The implicit systems are given by \(E \dot{x} = A x + B u, y = Cx\), and \(0=D_i x\), \(i =1,\ldots,n\). The central problem is whether there exists a feedback \(u = F_p x + F_d \dot{x}\) such that the same external closed-loop behavior is assigned to all \(n\) systems. For a single system the problem has been solved by \textit{M. Bonilla}, \textit{G. Lebret} and \textit{M. Malabre} [Circuits Syst. Signal Process. 13, No. 2--3, 349--359 (1994; Zbl 0806.93009)]. The authors find the common internal structure which enables them to solve the above problem. Like in Bonilla et al.\ the problem is solved via the geometric approach.