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A Brauer’s theorem and related results

Rafael Bru, Rafael Cantó, Ricardo Soto, Ana Urbano (2012)

Open Mathematics

Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system...

A new approach to generalized chaos synchronization based on the stability of the error system

Zhi Liang Zhu, Shuping Li, Hai Yu (2008)

Kybernetika

With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity....

A new indirect adaptive pole placer for possibly non-minimum phase MIMO linear systems

Kostas G. Arvanitis, Grigoris Kalogeropoulos, I. K. Kookos (2000)

Kybernetika

The use of generalized sampled-data hold functions, in order to synthesize adaptive pole placers for linear multiple-input, multiple-output systems with unknown parameters, is investigated in this paper, for the first time. Such a control scheme relies on a periodically varying controller, which suitably modulates the sampled outputs of the controlled plant. The proposed control strategy allows us to assign the poles of the sampled closed-loop system arbitrarily in desired locations, and does not...

An LPV pole-placement approach to friction compensation as an FTC problem

Ron J. Patton, Lejun Chen, Supat Klinkhieo (2012)

International Journal of Applied Mathematics and Computer Science

The concept of combining robust fault estimation within a controller system to achieve active Fault Tolerant Control (FTC) has been the subject of considerable interest in the recent literature. The current study is motivated by the need to develop model-based FTC schemes for systems that have no unique equilibria and are therefore difficult to linearise. Linear Parameter Varying (LPV) strategies are well suited to model-based control and fault estimation for such systems. This contribution involves...

Argument increment stability criterion for linear delta models

Milan Hofreiter, Pavel Zítek (2003)

International Journal of Applied Mathematics and Computer Science

Currently used stability criteria for linear sampled-data systems refer to the standard linear difference equation form of the system model. This paper presents a stability criterion based on the argument increment rule modified for the delta operator form of the sampled-data model. For the asymptotic stability of this system form it is necessary and sufficient that the roots of the appropriate characteristic equation lie inside a circle in the left half of the complex plane, the radius of which...

Closed-loop structure of decouplable linear multivariable systems

Javier Ruiz, Jorge Luis Orozco, Ofelia Begovich (2005)

Kybernetika

Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized, which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined,...

Deadbeat control, pole placement, and LQ regulation

Vladimír Kučera (1999)

Kybernetika

Deadbeat control, a typical example of linear control strategies in discrete- time systems, is shown to be a special case of the linear-quadratic regulation. This result is obtained by drawing on the parallels between the state-space and the transfer-function design techniques.

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.

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