Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces

1989 ◽

Vol 12 (1) ◽

pp. 175-191 ◽

Cited By ~ 9

Author(s):

Nikolaos S. Papageorgiou

Keyword(s):

Control Systems ◽

Banach Spaces ◽

Time Dependent ◽

Linear Control ◽

Linear Control Systems ◽

Integral Functionals ◽

Control Constraints ◽

Infinite Dimensional ◽

Measurable Multifunctions

The purpose of this paper is to establish some new properties of set valued measurable functions and of their sets of Integrable selectors and to use them to study convex integral functionals defined on Lebesgue-Bochner spaces. In this process we also obtain a characterization of separable dual Banach spaces using multifunctions and we present some generalizations of the classical “bang-bang” principle to infinite dimensional linear control systems with time dependent control constraints.

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On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽

10.3390/math9020116 ◽

2021 ◽

Vol 9 (2) ◽

pp. 116

Author(s):

Qi Liu ◽

Yongjin Li

Keyword(s):

Banach Spaces ◽

Product Space ◽

Sufficient Conditions ◽

Normal Structure ◽

The Other ◽

Inner Product ◽

Equivalent Characterization ◽

Geometric Constant ◽

Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

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A Functional Characterization of Almost Greedy and Partially Greedy Bases in Banach Spaces

Mathematics ◽

10.3390/math9151827 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1827

Author(s):

Pablo Manuel Berná ◽

Diego Mondéjar

Keyword(s):

Banach Spaces ◽

Functional Characterization

In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness). In this paper, we show a new functional characterization of these type of bases in general Banach spaces following the spirit of the characterization of greediness proved in 2017 by P. M. Berná and Ó. Blasco.

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Sets of periods for chaotic linear operators

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas ◽

10.1007/s13398-020-00996-z ◽

2021 ◽

Vol 115 (2) ◽

Author(s):

J. A. Conejero ◽

F. Martínez-Giménez ◽

A. Peris ◽

F. Rodenas

Keyword(s):

Banach Spaces ◽

Hilbert Spaces ◽

Complete Characterization ◽

Linear Operators

AbstractWe provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.

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Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

Advances in Difference Equations ◽

10.1186/s13662-021-03373-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

M. Mohan Raja ◽

V. Vijayakumar ◽

Le Nhat Huynh ◽

R. Udhayakumar ◽

Kottakkaran Sooppy Nisar

Keyword(s):

Fixed Point ◽

Control Systems ◽

Approximate Controllability ◽

Hemivariational Inequalities ◽

Evolution Inclusions ◽

Fractional Systems ◽

Cosine Families ◽

Fixed Point Approach ◽

Semilinear Control Systems ◽

Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

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