On uniform exponential stability of periodic evolution operators in Banach spaces.
Megan, M., Sasu, L., Sasu, B. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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Megan, M., Sasu, L., Sasu, B. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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Tervo, J., Nihtilä, M. (2000)
Zeitschrift für Analysis und ihre Anwendungen
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Naoki Tanaka (2001)
Studia Mathematica
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A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.
Michael I. Gil' (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady...
Zhang Li, Gang Yu, Yanjun Shen (2021)
Kybernetika
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In this paper, we discuss exponential stability for nonlinear systems with sampled-data-based event-triggered schemes. First, a framework is proposed to analyze exponential stability for nonlinear systems under some different triggering conditions. Based on these results, output feedback exponential stabilization is investigated for a class of inherently nonlinear systems under a kind of event-triggered strategies. Finally, the rationality of the theoretical work is verified by numerical...
Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu (2003)
Archivum Mathematicum
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In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.
Sasu, Adina Luminiţa (2010)
Advances in Difference Equations [electronic only]
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Zhonghuai Wu, Jianying Shao, Mingquan Yang, Wei Gao (2011)
Annales Polonici Mathematici
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We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].
Preda, P., Pogan, A., Preda, C. (2005)
Acta Mathematica Universitatis Comenianae. New Series
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Aissa Guesmia (2017)
Nonautonomous Dynamical Systems
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The asymptotic stability of one-dimensional linear Bresse systems under infinite memories was obtained by Guesmia and Kafini [10] (three infinite memories), Guesmia and Kirane [11] (two infinite memories), Guesmia [9] (one infinite memory acting on the longitudinal displacement) and De Lima Santos et al. [6] (one infinite memory acting on the shear angle displacement). When the kernel functions have an exponential decay at infinity, the obtained stability estimates in these papers lead...
Buşe, C. (2001)
Rendiconti del Seminario Matematico
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Buşe, Constantin (2003)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Abdoua Tchousso, Thibaut Besson, Cheng-Zhong Xu (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering...