Model reduction via truncation: An interpolation point of view. (Q1414700)

A linear time-invariant continuous system is considered, characterized by the matrices \(A\), \(B\), \(C\) and \(D\), where \(A\) is a square matrix of dimension \(N\), \(B\), \(C\) and \(D\) being of dimension \((N,m)\), \((p,N)\) and \((p,m)\), respectively, and with input \(u(t)\) and output \(y(t)\). Here the order \(N\) is assumed to be quite large. In this case the system is approximated by a reduced-order system with the same input \(u(t)\) but a different output \(y^*(t)\) and now characterized by the matrices \(A^*\), \(B^*\), \(C^*\) and \(D^*\), \(A^*\) being a square matrix of dimension \(n\), so that the degree \(n\) of the new system is much smaller than \(N\). The main aim of the work consists in finding a reduced model such that the transfer functions of both models, namely \(T(s)\) and \(T^*(s)\), satisfy that the error \(\| T(.)- T^*(.)\|\) is minimal for the \(H_\infty\) norm. A method constructed via truncation of the expansion of the matrix function \(T(s)\) is presented and its convergence analyzed making use of certain multipoint Padé interpolation properties.