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A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

Lan Zhou, Jinhua She, Shaowu Zhou (2014)

International Journal of Applied Mathematics and Computer Science

This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic outputfeedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value...

A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators

Qi Lü (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This result is a consequence of a new pointwise and weighted estimate for Laplace-Beltrami operators, a construction of some nonnegative function with arbitrary given critical point location in the manifold, and also two interpolation results for solutions of elliptic equations with lateral...

An extension of the Cayley-Hamilton theorem for nonlinear time-varying systems

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

The classical Cayley-Hamilton theorem is extended to nonlinear time-varying systems with square and rectangular system matrices. It is shown that in both cases system matrices satisfy many equations with coefficients being the coefficients of characteristic polynomials of suitable square matrices. The proposed theorems are illustrated with numerical examples.

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