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Szegő's first limit theorem in terms of a realization of a continuous-time time-varying systems

100%
Iglesias P. A., Zang G.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 6
1261-1276
EN
It is shown that the limit in an abstract version of Szegő's limit theorem can be expressed in terms of the antistable dynamics of the system. When the system dynamics are regular, it is shown that the limit equals the difference between the antistable Lyapunov exponents of the system and those of its inverse. In the general case, the elements of the dichotomy spectrum give lower and upper bounds.
2
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On the discrete time-varying JLQG problem

100%
Czornik A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 2
203-207
EN
In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.
3
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The geometry of Darlington synthesis (in memory of W. Cauer)

88%
Dewilde P.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 6
1379-1386
EN
We revisit the classical problem of 'Darlington synthesis', or Darlington embedding. Although traditionally it is solved using analytic means, a more natural way to approach it is to use the geometric properties of a well-chosen Hankel map. The method yields surprising results. In the first place, it allows us to formulate necessary and sufficient conditions for the existence of the embedding in terms of systems properties of the transfer operation to be embedded. In addition, the approach allows us to extend the solution to situations where no analytical transform is available. The paper has a high review content, as all the results presented have been obtained during the last twenty years and have been published. However, we make a systematic attempt at formulating them in a geometric way, independent of an accidental parametrization. The benefit is clarity and generality.
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