Gas-discharge XeF* (B→X) laser with high specific output energy

The discharge characteristics of the XeF* (B→X) laser are investigated. The NF3 and Xe partial pressure of the laser gas mixture and the total gas pressure have been varied. A highest specific output energy of 4.7 J/l with an efficiency of 0.5% was obtained from a X-ray preionized Ne/Xe/NF3 gas mixture at 6 bar with single-pulse excitation through a multichannel spark gap

The behavioral approach to systems and modeling

An introduction to behavioral system theory, and a brief review of the content of the Special Issue are given

Hamiltonian and Variational Linear Distributed Systems

We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary linear constant-coefficient differential equations is Hamiltonian if and only if it is variational. In this paper we extend this result to systems described by linear, constant-coefficient partial differential equations. It is shown that any variational system is Hamiltonian, and that any scalar Hamiltonian system is contained (in general, properly) in a particular variational system

Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation

We study the existence of positive and negative semidefinite solutions of algebraic Riccati equations (ARE) corresponding to linear quadratic problems with an indefinite cost functional. The problem to formulate reasonable necessary and sufficient conditions for the existence of such solutions is a long-standing open problem. A central role is played by certain two-variable polynomial matrices associated with the ARE. Our main result characterizes all unmixed solutions of the ARE in terms of the Pick matrices associated with these two-variable polynomial matrices. As a corollary of this result we obtain that the signatures of the extremal solutions of the ARE are determined by the signatures of particular Pick matrices

Linear Hamiltonian behaviors and bilinear differential forms

We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences and allows us to study systems described by higher-order differential equations, thus dispensing with the usual point of view in classical mechanics of considering first- and second-order differential equations only

The Kalman-Yakubovich-Popov lemma in a behavioural framework

The classical Kalman-Yakubovich-Popov Lemma provides a link between dissipativity of a system in state-space form and the solution to a linear matrix inequality. In this paper we derive the KYP Lemma for linear systems described by higher-order differential equations. The result is an LMI in terms of the original coefficients in which the dissipativity problem is posed. Subsequently we study the connection between dissipativity and spectral factorization of polynomial matrices. This enables us to derive a new algorithm for polynomial spectral factorization in terms of an LMI in the coefficients of a polynomial matrix

Dissipativity preserving model reduction by retention of trajectories of minimal dissipation

We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced order model is required to reproduce a subset of the set of trajectories of minimal dissipation of the original system. The passivity-preserving model reduction method of Antoulas (Syst Control Lett 54:361-374, 2005) and Sorensen (Syst Control Lett 54:347-360, 2005) is shown to be a particular case of this more general class of model reduction procedures

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless- or dissipative system from a given noise-free trajectory; important special cases are passive- and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; state-space equations are then computed solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order mode

Model Reduction for Controllable Systems

In the papers [1], [7] a new scheme for passivity-preserving model reduction has been proposed. We have shown in [2] that the approach can also be interpreted from a dissipativity theory point of view, and we put forward two procedures in order to compute a driving variable or output nulling representation of a reduced order model for a given behavior. In this paper we illustrate improved versions of both algorithms, which produce a controllable reduced-order model. The new algorithms are based on several original results of independent interest