Abstract: Recently a method of model reduction for discrete systems has been proposed in the literature based on a new impulse response Gramian. In this method, the system matrix Ar of a reduced model is computed by approximating the reduced-order impulse response Gramian. The remaining matrices br and cr are obtained so that various initial Markov parameters and time-moments of the original sy...

The complexity of gene regulatory networks described by coupled nonlinear differential equations is often an obstacle for analysis purposes. They are prone to internal parametrical fluctuations making thus robustness a crucial property of these networks to attenuate the effects of internal fluctuation. Therefore, the development of effective model reduction techniques for uncertain biological s...

Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so called system Gramian matrices were developed in linear system theory for applications such as model order reduction of control systems. Empirical Gramian matrices are an extension to the system Gramians for parametric and nonlinear systems as well as ...

The Networked Embedded Control System (NECS) uses communication networks in the feedback loops. Since the embedded systems have the limited battery power along with limited bandwidth and computing power, the feedback data rates are limited. The rate of communications can drastically affect system stability. Hence, there is a strong need for understanding and merging the Control Theory with Comm...

Article history: Received 16 October 2007 Accepted 3 April 2008

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

In this work, we deal with normalizable-balanced singular systems, that is, singular systems where the obtained closed-loop system is balanced by an appropriate feedback. In the invariant case, we use a proportional and derivative feedback to obtain systems without infinite poles. In addition, the existence and construction of state-feedbacks to obtain normalizable-balanced N-periodic singular ...

In this paper we consider the standard linear SDP problem, and its low rank nonlinear programming reformulation, based on a Gramian representation of a positive semidefinite matrix. For this nonconvex quadratic problem with quadratic equality constraints, we give necessary and sufficient conditions of global optimality expressed in terms of the Lagrangian function.