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Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

Mouffak Benchohra, Lech Górniewicz, Sotiris K. Ntouyas (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.

Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance

Eugene P. Ryan, Chris J. Sangwin, Philip Townsend (2009)

ESAIM: Control, Optimisation and Calculus of Variations

A tracking problem is considered in the context of a class 𝒮 of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, m -input, m -output, minimum-phase systems with sign-definite “high-frequency gain”. The first control objective is tracking of reference signals r by the output y of any system in 𝒮 : given λ 0 , construct a feedback strategy which ensures that, for every r (assumed bounded...

Controlled functional differential equations: approximate and exact asymptotic tracking with prescribed transient performance

Eugene P. Ryan, Chris J. Sangwin, Philip Townsend (2008)

ESAIM: Control, Optimisation and Calculus of Variations

A tracking problem is considered in the context of a class 𝒮 of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, m-input, m-output, minimum-phase systems with sign-definite “high-frequency gain". The first control objective is tracking of reference signals r by the output y of any system in 𝒮 : given λ 0 , construct a feedback strategy which ensures that, for every r (assumed bounded with...

Convergence of numerical methods for systems of neutral functional-differential-algebraic equations

Tadeusz Jankowski, Marian Kwapisz (1995)

Applications of Mathematics

A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.

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