Duality and singular value functions of the nonlinear normalized right and left coprime factorizations

This paper considers the nonlinear left coprime factorization (NLCF) of a nonlinear system. In order to study the balanced realization of such NLCF first a dual system notion is introduced. The important energy functions for the original NLCF and their relation with the dual NLCF are studied and relations between these functions are established. These developments can be used for studying a relation between the singular value functions of the NLCF and the normalized right coprime factorization (NRCF) of a nonlinear system. The singular value functions are a useful tool for model reduction of unstable nonlinear systems.

Balancing and model reduction for discrete-time nonlinear systems based on Hankel singular value analysis

This paper is concerned with balanced realization and model reduction for discrete-time nonlinear systems. Singular perturbation type balanced truncation method is proposed. In this procedure, the Hankel singular values and the related controllability and observability properties are preserved, which is a natural generalization of both the linear discrete-time case and the nonlinear continuous-time case.

A power-based perspective of mechanical systems

This paper is concerned with the construction of a power-based modeling framework for a large class of mechanical systems. Mathematically this is formalized by proving that every standard mechanical system (with or without dissipation) can be written as a gradient vector field with respect to an indefinite metric. The form and existence of the corresponding potential function is shown to be the mechanical analogue of Brayton and Moser's mixed-potential function as originally derived for nonlinear electrical networks in the early sixties. In this way, several recently proposed analysis and control methods that use the mixed-potential function as a starting point can also be applied to mechanical systems.

Nonlinear input-normal realizations based on the differential eigenstructure of hankel operators

This paper investigates the differential eigenstructure of Hankel operators for nonlinear systems. First, it is proven that the variational system and the Hamiltonian extension with extended input and output spaces can be interpreted as the Gâteaux differential and its adjoint of a dynamical input-output system, respectively. Second, the Gâteaux differential is utilized to clarify the main result the differential eigenstructure of the nonlinear Hankel operator which is closely related to the Hankel norm of the original system. Third, a new characterization of the nonlinear extension of Hankel singular values are given based on the differential eigenstructure. Finally, a balancing procedure to obtain a new input-normal/output-diagonal realization is derived. The results in this paper thus provide new insights to the realization and balancing theory for nonlinear systems.

Nonlinear cross Gramians and gradient systems

We study the notion of cross Gramians for non-linear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.

Gradient System Modelling of Matrix Converters with Input and Output Filters

Due to its complexity, the dynamics of matrix converters are usually neglected in controller design. However, increasing demands on reduced harmonic generation and higher bandwidths makes it necessary to study large-signal dynamics. A unified methodology that considers matrix converters, including input and output filters, as gradient systems is presented.

Passivity-based harmonic control through series/parallel damping of an H-bridge rectifier

Nowadays the H-bridge is one of the preferred solutions to connect DC loads or distributed sources to the single-phase grid. The control aims are: sinusoidal grid current with unity power factor and optimal DC voltage regulation capability. These objectives should be satisfied, regardless the conditions of the grid, the DC load/source and the converter nonlinearities. In this paper a passivity-based approach is thoroughly investigated proposing a damping-based solution for the error dynamics. Practical experiments with a real converter validate the analysis.