This paper examines the system dynamics of a controlled networked multi-agent system, operating with a consensus-type algorithm, that is under the influence of attached node(s). We introduce an identification scheme, involving excitation and observation of the network by the attached node(s), that identifies the spectrum of the underlying system matrix in this case the influenced network’s modi...

In this paper a general framework is posed for defining the reachability and controllability gramians of structured linear dynamical systems. The novelty is that a formula for the gramian is given in the frequency domain. This formulation is surprisingly versatile and may be applied in a variety of structured problems. Moreover, this formulation enables a rather straightforward development of a...

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from the recent work [13]. We study controllability in terms of the controllability Gramian and vari...

In this first part, analytical methods for finding moments of random Vandermonde matrices are developed. Vandermonde Matrices play an important role in signal processing and communication applications such as direction of arrival estimation, precoding or sparse sampling theory for example. Within this framework, we extend classical freeness results on random matrices with i.i.d entries and show...

Model order deduction algorithms have been developed in an effort to automate the production of accurate, minimal complexity models of dynamic systems in order to aid in the design of these systems. Previous algorithms, MODA and Extended MODA, deduce models independent of system inputs and outputs. FD-MODA uses frequency response methods to deduce models of a single input-output pair. In this p...

In this paper, a general method for model order reduction of discrete-time switched linear systems is presented. The proposed technique uses switching generalized gramians. It is shown that several classical reduction methods can be developed into the generalized gramian framework for the model reduction of linear systems and for the reduction of switched systems. Discrete-time balanced reducti...

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result i...

Abstract. The properties of oversampled affine frames are considered here with two main goals in mind. The first goal is to generalize the approach of Chui and Shi to the matrix oversampling setting for expanding, lattice-preserving dilations, whereby we obtain a new proof of the Second Oversampling Theorem for affine frames. The Second Oversampling Theorem, proven originally by Ron and Shen vi...

In this work, the empirical-Gramian-based model reduction methods: Empirical poor man’s truncated balanced realization, empirical approximate balancing, dominant subspaces, truncation, and gains are compared in a non-parametric two parametric variants, via ten error measures: Approximate Lebesgue \(L_0\), \(L_1\), \(L_2\), \(L_\infty \), Hardy \(H_2\), \(H_\infty Hankel, Hilbert-Schmidt-Hankel,...