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.

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 $V\in L^{\infty }\left({𝕋}^n\right)$.

We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.

Interpretations of most existing controllability and observability notions for linear delay systems are given. Module theoretic characterizations are presented. This setting enables a clear and precise comparison of the various examined notions. A new notion of controllability is introduced, which is called pi-freeness.

In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.

In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.

We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data....

This article aims at studying the controllability of a simplified fluid structure interaction model derived and developed in [C. Conca, J. Planchard and M. Vanninathan, RAM: Res. Appl. Math. John Wiley & Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, ESAIM: COCV 11 (2005) 180–203; M. Tucsnak and M. Vanninathan, Systems Control Lett. 58 (2009) 547–552]. This interaction is modeled by a wave equation surrounding a harmonic oscillator. Our main result states that, in the radially...

We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d wave equation in the square. We prove the uniform (with respect to the meshsize) boundary observability for the solutions obtained by the two-grid preconditioner introduced by Glowinski [9]. Our method uses previously known uniform observability inequalities for low frequency solutions and a dyadic spectral time decomposition. As a consequence we prove the convergence of the two-grid algorithm...