Controllability indices for structured systems (Q5961587)

Linear time-invariant multivariable control systems having a structure that reflects vanishing/nonvanishing interactions are often described in terms of pairs of matrices \((A,B)\), where \(A\) is \(n\times n\), \(B\) is \(n\times m\), and where certain fixed positions in these matrices are assumed to be zero. In the reviewed paper, for such structured systems, controllability indices are characterized, and a procedure is given to calculate these indices and to identify the input variable associated with every controllability index. The procedure is based on a description of the structured systems in terms of directed graphs.