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Browsing by Subject "exponential stability"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Datko-type theorems concerning asymptotic behaviour of exponential type in mean
    (Wydawnictwa AGH, 2025) Hai, Pham Viet
    In this paper, we study the concept of exponential (in)stability in mean for stochastic skew-evolution semiflows, in which the exponential (in)stability in the classical sense is replaced by an average with respect to a probability measure. Our paper consists of three major results. The first is to obtain Datko-type characterizations for the exponential stability in mean of stochastic skew-evolution semiflows. Next, we acquire Datko-type characterizations for the exponential instability in mean by extending the stability techniques. The last is to extend Lyapunov-type equations to the case of exponential (in)stability in mean.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Exponential stability results for variable delay difference equations
    (Wydawnictwa AGH, 2021) Yankson, Ernest
    Sufficient conditions that guarantee exponential decay to zero of the variable delay difference equation $x(n+1)=a(n)x(n)+b(n)x(n-g(n))$ are obtained. These sufficient conditions are deduced via inequalities by employing Lyapunov functionals. In addition, a criterion for the instability of the zero solution is established. The results in the paper generalizes some results in the literature.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Polynomial stability of evolution operators in Banach spaces
    (2011) Megan, Mihail; Ceauşu, Traian; Ramneanţu, Magda Luminiţa
    The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.