Null controllability of some impulsive evolution equation in a Hilbert space.
Boukhamla, R., Mazouzi, S. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Boukhamla, R., Mazouzi, S. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Vijayakumar S. Muni, Raju K. George (2020)
Kybernetika
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This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix...
N.U. Ahmed (2004)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point...
Rathinasamy Sakthivel (2009)
International Journal of Applied Mathematics and Computer Science
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In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.
Khalil Ezzinbi, Guy Degla, Patrice Ndambomve (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang,...
Michał Kisielewicz (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
L. Górniewicz, S. K. Ntouyas, D. O'Regan (2006)
Annales Polonici Mathematici
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We prove controllability results for first and second order semilinear differential inclusions in Banach spaces with nonlocal conditions.
Jerzy Klamka (2007)
International Journal of Applied Mathematics and Computer Science
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A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability...
Shanmugasundaram Karthikeyan, Krishnan Balachandran (2011)
International Journal of Applied Mathematics and Computer Science
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This paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.
Vikas Kumar Mishra, Nutan Kumar Tomar (2017)
Kybernetika
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Contrary to state space systems, there are different notions of controllability for linear time invariant descriptor systems due to the non smooth inputs and inconsistent initial conditions. A comprehensive study of different notions of controllability for linear descriptor systems is performed. Also, it is proved that reachable controllability for general linear time invariant descriptor system is equivalent to the controllability of some matrix pair under an assumption milder than...
Jerzy Klamka (1996)
Kybernetika
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Krishnan Balachandran, Rathinasamy Sakthivel (2000)
Kybernetika
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Sufficient conditions for controllability of semilinear functional integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.