Related papers: A unified observability result for non-autonomous …
We consider linear control systems of the form $\dot{y}(t)=Ay(t)-\mu B C y(t)$ where $\mu$ is a positive real parameter, $A$ is the state operator and generates a linear $C_0-$semigroup of contractions $S(t) $ on a Banach space $X$, $B$ and…
In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with…
For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We…
We show that if $X$ is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping $f\colon X\to X$ such that the autonomous…
In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous…
This paper is concerned with the notions of admissibility, exact controllability, exact observability and regularity of linear systems in the Banach space setting. It is proved that admissible controllability, exact controllability,…
The problem of state estimation has a long history with many successful algorithms that allow analytical derivation or approximation of posterior filtering distribution given the noisy observations. This report tries to conclude previous…
We establish two fixed point theorems for certain mappings of contractive type. The first result is concerned with the case where such mappings take a nonempty, closed subset of a complete metric space $X$ into $X$, and the second with an…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
The paper deals with the observer design problem for a wide class of triangular time-varying nonlinear systems, with unobservable linearization. Sufficient conditions are derived for the existence of a Luenberger-type observer, when it is a…
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators.…
We review the current state of the homogeneous Banach space problem. We then formulate several questions which arise naturally from this problem, some of which seem to be fundamental but new. We give many examples defining the bounds on the…
This work is concerned with the distributed controllability of the one-dimensional wave equation over non-cylindrical domains. The controllability in that case has been obtained in [Castro-Cindea-Munch, Controllability of the linear…
This paper presents results on the solvability of the observer design problem for general nonlinear triangular systems with inputs, under weak observability assumptions. The local state estimation is exhibited by means of a delayed…
Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania…
This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution…
In this work I study the well-posedness of the Cauchy problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities}, which appears modeling problems in nonlinear optics. I obtain the local well-posedness for…