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Weak regularizability and pole assignment for non-square linear systems

Tetiana Korotka, Jean-Jacques Loiseau, Petr Zagalak (2012)

Kybernetika

The problem of pole assignment by state feedback in the class of non-square linear systems is considered in the paper. It is shown that the problem is solvable under the assumption of weak regularizability, a newly introduced concept that can be viewed as a generalization of the regularizability of square systems. Necessary conditions of solvability for the problem of pole assignment are established. It is also shown that sufficient conditions can be derived in some special cases. Some conclusions...

Weak structure at infinity and row-by-row decoupling for linear delay systems

Rabah Rabah, Michel Malabre (2004)

Kybernetika

We consider the row-by-row decoupling problem for linear delay systems and show some close connections between the design of a decoupling controller and some particular structures of delay systems, namely the so-called weak structure at infinity. The realization by static state feedback of decoupling precompensators is studied, in particular, generalized state feedback laws which may incorporate derivatives of the delayed new reference.

Well-posed linear systems - a survey with emphasis on conservative systems

George Weiss, Olof Staffans, Marius Tucsnak (2001)

International Journal of Applied Mathematics and Computer Science

We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space....

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

Zeros in linear systems with time delay in state

Jerzy Tokarzewski (2009)

International Journal of Applied Mathematics and Computer Science

The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount...

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