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Attractors of strongly dissipative systems

100%

Ramm A. G.

2009

tom Vol. 57, no 1

25-31

A class of infinite-dimensional dissipative dynamical systems is denned for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947 (83m:45002)).

Factorization of the Popov function of a multivariable linear distributed parameter system in the non-coercive case: a penalization approach

100%

Pandolfi L.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 6

1249-1260

We study the construction of an outer factor to a positive definite Popov function of a distributed parameter system. We assume that is a non-negative definite matrix with non-zero determinant. Coercivity is not assumed. We present a penalization approach which gives an outer factor just in the case when there exists any outer factor.

Factorization of the Popov Function of a Multivariable Linear Distributed Parameter System in the Non-Coercive Case: a Penalization Approach

86%

Pandolfi L.

2001

tom Vol. 11, no 6

1249-1260

We study the construction of an outer factor to a positive definite Popov function Pi(iomega) of a distributed parameter system. We assume that Pi(iomega) is a non-negative definite matrix with non-zero determinant. Coercivity is not assumed. We present a penalization approach which gives an outer factor just in the case when there exists any outer factor.

J-energy preserving well-posed linear systems

58%

Staffans O. J.

2001

tom Vol. 11, no 6

1361-1378

The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE's, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foias. The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems (H2- and Hinfty-theories).