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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.

Bounded-input-bounded-state stabilization of switched processes and periodic asymptotic controllability

Andrea Bacciotti (2017)

Kybernetika

The main result of this paper is a sufficient condition for the existence of periodic switching signals which render asymptotically stable at the origin a linear switched process defined by a pair of 2 × 2 real matrices. The interest of this result is motivated by the application to the problem of bounded-input-bounded-state (with respect to an external input) stabilization of linear switched processes.

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

Mikołaj Busłowicz, Andrzej Ruszewski (2012)

International Journal of Applied Mathematics and Computer Science

Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

Control of the underactuated mechanical systems using natural motion

Zdeněk Neusser, Michael Valášek (2012)

Kybernetika

The paper deals with the control of underactuated mechanical systems between equilibrium positions across the singular positions. The considered mechanical systems are in the gravity field. The goal is to find feasible trajectory connecting the equilibrium positions that can be the basis of the system control. Such trajectory can be stabilized around both equilibrium positions and due to the gravity forces the mechanical system overcomes the singular positions. This altogether constitutes the control...

Controllability of a slowly rotating Timoshenko beam

Martin Gugat (2001)

ESAIM: Control, Optimisation and Calculus of Variations

Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd...

Controllability of a slowly rotating Timoshenko beam

Martin Gugat (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an...

Controllable graphs

D. Cvetković, P. Rowlinson, Z. Stanić, M. G. Yoon (2011)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Data-driven models for fault detection using kernel PCA: A water distribution system case study

Adam Nowicki, Michał Grochowski, Kazimierz Duzinkiewicz (2012)

International Journal of Applied Mathematics and Computer Science

Kernel Principal Component Analysis (KPCA), an example of machine learning, can be considered a non-linear extension of the PCA method. While various applications of KPCA are known, this paper explores the possibility to use it for building a data-driven model of a non-linear system-the water distribution system of the Chojnice town (Poland). This model is utilised for fault detection with the emphasis on water leakage detection. A systematic description of the system's framework is followed by...

Decoupling and pole assignment by constant output feedback

Konstadinos H. Kiritsis, Trifon G. Koussiouris (2002)

Kybernetika

In this paper a system-theoretic approach is used to solve the decoupling in combination with the arbitrary pole assignment problem by constant output feedback and a constant nonsingular input transformation. Explicit necessary and sufficient conditions are given and a procedure is described for the determination of the control law.

Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix

Imran Rashid, Martin Gavalec, Sergeĭ Sergeev (2012)

Kybernetika

Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to...

Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks

Tadeusz Kaczorek (2001)

International Journal of Applied Mathematics and Computer Science

A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.

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