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.

Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.

Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.

The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems.

Maps $f$ defined on the interior of the standard non-negative cone $K$ in ${ℝ}^N$ which are both homogeneous of degree $1$ and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least...

The problem of obtaining a continuous-time (i. e., ripple-free) input-output decoupled control system for a continuous-time linear time-invariant plant, by means of a purely discrete-time compensator, is stated and solved in the case of a unity feedback control system. Such a control system is hybrid, since the plant is continuous-time and the compensator is discrete-time. A necessary and sufficient condition for the existence of a solution of such a problem is given, which reduces the mentioned...

The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of $H_2$ and $H_{\infty }$ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in $H_2$ and $H_{\infty }$ are introduced and solved.

This paper deals with some state-feedback $H_2/H_{\infty }$ control problems for continuous time periodic systems. The derivation of the theoretical results underlying such problems has been presented in the first part of the paper. Here, the parametrization and optimization problems in $H_2$, $H_{\infty }$ and mixed $H_2/H_{\infty }$ are introduced and solved.

Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states....

We seek to classify the full-rank left-invariant control affine systems evolving on solvable three-dimensional Lie groups. In this paper we consider only the cases corresponding to the solvable Lie algebras of types II, IV, and V in the Bianchi-Behr classification.

For the Schrödinger equation, $(i{\partial }_t+\nabla )u=0$ on a torus, an arbitrary non-empty open set $\Omega$ provides control and observability of the solution: $∥u{\left|{}_{t=0}\right.∥}_{L^2\left({𝕋}^2\right)}\le K_T{∥u∥}_{L^2([0,T]\times \Omega )}$. We show that the same result remains true for $(i{\partial }_t+\nabla -V)u=0$ where $V\in L^2\left({𝕋}^2\right)$, and ${𝕋}^2$ is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for $V\in C\left({𝕋}^2\right)$ and conjectured for $V\in L^{\infty }\left({𝕋}^2\right)$. The higher dimensional generalization remains open for $V\in L^{\infty }\left({𝕋}^n\right)$.

For a general time-varying system, we prove that existence of an “Output Robust Control Lyapunov Function” implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well known result due to Coron and Rosier [J. Math. Syst. Estim. Control 4 (1994) 67–84] concerning stabilization of autonomous systems by means of time-varying periodic...

For a general time-varying system, we prove that existence of an “Output Robust Control Lyapunov Function” implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well known result due to Coron and Rosier [J. Math. Syst. Estim. Control4 (1994) 67–84] concerning stabilization of autonomous systems by means of time-varying...

A control system of the second order in time with control $u=u\left(t\right)\in L^2([0,T];U)$ is considered. If the system is controllable in a strong sense and uT is the control steering the system to the rest at time T, then the L2–norm of uT decreases as $1/\sqrt{T}$ while the $L^1([0,T];U)$–norm of uT is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.

We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate these results with numerical simulations.