This paper deals with diagonal systems on a Hilbert space with a onedimensional input space and a (possibly unbounded) input operator. A priori it is not assumed that the input operator is admissible. Necessary and sufficient conditions for different notions of controllability such as null controllability and exact controllability are presented. These conditions, which are given in terms of the...

This note uses a polynomial approach to present a necessary and sufficient condition for local controllability of single-input– single-output (SISO) nonlinear systems. The condition is presented in terms of common factors of a noncommutative polynomial expression. This result exposes controllability properties of a nonlinear system in the input–output framework, and gives a computable procedure...

In this paper we study controllability properties for semilinear degenerate parabolic equations with nonlinearities involving the first derivative in a bounded domain of R. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of ’regional null controllability’, showing that we can drive the solution to rest at time T on a subset of the sp...

Families of regimes for discrete control systems are studied possessing a special quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the amplitudes of transient regimes in quasi-controllable systems. Its essence is in obtaining of constructive a priori bounds for degree of overshooting in terms of the quasi-controllabili...

Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the contr...

This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel operators, and controllability and observability functions will be derived based on it. Furthermore ...

Controllability and observability of analytically solvable linear time-varying singular systems are considered. Our analysis includes the possible impulsive zero-input response. Based on the definitions of controllability and observability naturally extended from the ones adopted in the time-invariant setting, sufficient and necessary conditions for these two properties are derived. Furthermore...

We address the question of exact controllability of the wave and Schrödinger equations perturbed by a singular inverse-square potential. Exact boundary controllability is proved in the range of subcritical coefficients of the singular potential and under suitable geometric conditions. The proof relies on the method of multipliers. The key point in the proof of the observability inequality is a ...

In this paper we study the dynamic path controllability of discrete-time nonlinear economic models in state-space form. First we present an algorithmic procedure for testing this property for time-varying linear systems. Secondly we extend this method to general nonlinear models and we show that under generic conditions path controllability around a specific trajectory of the nonlinear system i...

We deal with the approximate controllability of control systems governed by delayed semilinear differential equations ẏ(t) =Ay(t) +A1y(t−∆) +F(t, y(t), yt) + (Bu)(t). Various sufficient conditions for approximate controllability have been obtained; these results usually require some complicated and limited assumptions. Results in this paper provide sufficient conditions for the approximate cont...