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Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces

Viorica Mariela Ungureanu (2004)

Bollettino dell'Unione Matematica Italiana

In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.

Unifying approach to observer-filter design

Václav Černý (2009)

Kybernetika

The paper examines similarities between observer design as introduced in Automatic Control Theory and filter design as established in Signal Processing. It is shown in the paper that there are obvious connections between them in spite of different aims for their design. Therefore, it is prospective to make them be compatible from the structural point of view. Introduced error invariance and error convergence properties of both of them are unifying tools for their design. Lyapunov's stability theory,...

Upper bound estimation of the spectral abscissa for switched linear systems via coordinate transformations

Meili Lin, Zhendong Sun (2018)

Kybernetika

In this paper, we develop computational procedures to approximate the spectral abscissa of the switched linear system via square coordinate transformations. First, we design iterative algorithms to obtain a sequence of the least μ 1 measure. Second, it is shown that this sequence is convergent and its limit can be used to estimate the spectral abscissa. Moreover, the stopping condition of Algorithm 1 is also presented. Finally, an example is carried out to illustrate the effectiveness of the proposed...

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