A new decomposition method approach for strong and exponential stabilization of semilinear systems in banach spaces

This paper presents necessary and sufficient conditions for uniform exponential stabilization of a class of nonlinear systems in Banach state spaces. The stabilization assumptions are formulated in terms of integral estimates involving the control operator and the state of the uncontrolled version of the system at hand. An explicit estimate of the convergence speed is given. Applications to feedback stabilization of affine control systems are given. Illustrative examples are further provided.

Strong Asymptotic Stability of Linear Dynamical Systems in Banach Spaces

On null controllability of linear systems in Banach spaces

By an orthonormal system in a general complex Banach space, we mean a collection {eα: α ∈ } it vectors such that, for each α, there is an hermitian (in the numerical range sense, see (4)) projection Pα whose range is lin (eα) and such that PαPβ = 0, if α ≠ β. This paper is devoted to the study of orthonormal systems in general Banach spaces, and their applications to problems of characterizing isometries and hermitian operators.

Controllability of second-order integrodifferential evolution systems in Banach spaces

<p style='text-indent:20px;'>This paper presents a survey for some recent research on the controllability of nonlinear fractional evolution systems (FESs) in Banach spaces. The prime focus is exact controllability and approximate controllability of several types of FESs, which include the basic systems with classical initial and nonlocal conditions, FESs with time delay or impulsive effect. In addition, controllability results via resolvent operator are reviewed in detail. At last, the conclusions of this work and the research prospect are presented, which provides a reference for further study.</p>

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integro-differential systems in abstract spaces.

Controllability of Volterra–Fredholm type systems in Banach spaces

Controllability of second-order semilinear neutral functional differential systems in Banach spaces

This paper deals with the problem of stabilizability of perturbed linear time-varying control systems in Banach spaces. Assuming appropriate conditions on the perturbation term, it is shown that if every frozen-time control system is stabilizable then the corresponding non-autonomous control system is exponential stabilizable, provided the rate of variation of the system coefficient operators is sufficiently small. This approach is based on the extension of the freezing technique to infinite-dimensional Banach spaces. Sufficient conditions for the exponential feedback stabilizability of a class of time-varying nonlinear systems are established. The obtained results extend existing results in the literature to infinite-dimensional control systems.

Sufficient conditions for controllability of semilinear second order ordinary differential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results obtained are based on the Schaefer theorem.

A comment on the papers “A study on controllability of semilinear integrodifferential systems in banach spaces” and “controllability of neutral functional integrodifferential systems in banach spaces”

In this paper we are investigating boundedness and certain stability properties of differential systems in spaces, utilizing the generalization of Bellman's Lemma which was formulated by one of the authors (8).

Controllability of linear systems in Banach spaces

A class of boundary-distributed linear control systems in Banach spaces is studied. A maximum principle for a convex control problem associated with such systems is obtained.