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In this paper, we consider (large and complex) interconnected networks. We assume that each state/node, not belonging to a set of forbidden nodes of the network, can be selected to act as a steering node, meaning that such a node then is influenced by its own individual control. We aim to achieve structural controllability and we present a classification of the associated steering nodes as being essential (always required to be present), useful (present in certain configurations), and useless (never necessary in whatever configuration). The classification is based on two types of decomposition that naturally show up in the context of the two conditions (connection condition and rank condition) for structural controllability. The underlying methods are related to well known and efficient network algorithms. [ABSTRACT FROM AUTHOR]

The feedback stabilizability of a general class of well-posed linear systems with state and input delays in Banach spaces is studied in this paper. Using the properties of infinite dimensional linear systems, a necessary condition for the feedback stabilizability of delay systems is presented, which extends the well- known results for finite dimensional systems to infinite dimensional ones. This condition becomes sufficient as well if the semigroup of the delay-free system is immediately compact and the control space is finite dimensional. Moreover, under the condition that the Banach space is reflexive, a rank condition in terms of eigenvectors and control operators is proposed. When the delay-free state space and control space are all finite dimensional, a very compact rank condition is obtained. Finally, the abstract results are illustrated with examples. [ABSTRACT FROM AUTHOR]

This paper presents an iterative penalty function method for solving rank-constrained linear matrix inequality (LMI) problems and illustrates its application to reduced-order output feedback stabilization. We propose a penalized objective function to replace the rank condition, so that a solution to the original nonconvex LMI feasibility problem can be obtained by solving a series of convex LMI optimization subproblems. Numerical experiments were performed to demonstrate the proposed method. [ABSTRACT FROM AUTHOR]