GENERALIZED SAMPLED-DATA STABILIZATION OF WELL-POSED LINEAR INFINITE-DIMENSIONAL SYSTEMS ∗ (2008)
Hartmut Logemann, Richard Rebarber, Stuart Townley
Abstract. We consider well-posed linear infinite-dimensional systems, the outputs of which are sampled in a generalized sense using a suitable weighting function. Under certain natural assumptions on...
Robustness with respect to sampling for stabilization of Riesz spectral systems ∗ (2008)
Richard Rebarber, Stuart Townley
We suppose that a continuous-time feedback is input-output stabilizing for an infinite-dimensional system. We address the question of whether the sampled-data controller obtained by applying...
Kirsten Morris, Richard Rebarber
We consider a single-input single-output system on a Hilbert space X, with infinitesimal generator A, bounded control element b, and bounded observation element c. We consider the problem of finding...
Stability of infinite-dimensional sampled-data systems, preprint (2008)
Hartmut Logemann, Richard Rebarber, Stuart Townley, Hilbert Spaces
Abstract. Suppose that a static-state feedback stabilizes a continuous-time linear infinite-dimensional control system. We consider the following question: if we construct a sampled-data controller...
Hartmut Logemann, Claverton Down, Bath Ba Ay, Richard Rebarber
Abstract: In this paper we consider a large class of partial differential equations (PDEs) with distributed control and with a time-delay in the feedback loop. We analyze the relationship between the...
Low gain tracking for well-posed systems (2007)
Richard Rebarber, George Weiss
input-output stability; dynamic stabilization; structural
Kirsten Morris, Richard Rebarber
We give a definition of the zeros of an infinite-dimensional system with bounded control and observation operators B and C respectively. The zeros are defined in terms of the spectrum of an operator...
Hartmut Logemann, Bath Ba Ay, Richard Rebarber, Stuart Townley
Abstract: Suppose that a static state feedback stabilizes a continuous-time linear innite-dimensional control system. We consider the following question: if we construct a sampled-data controller by...
Hartmut Logemann, Richard Rebarber, George Weiss
Abstract: It has been observed that for many stable feedback control systems, the introduction of arbitrarily small time delays into the loop causes instability. In this paper we present a systematic...
Robustness With Respect to Sampling for Stabilization of Riesz Spectral Systems (2006)
Rebarber, Richard, Townley, Stuart
We suppose that a continuous-time feedback is input-output stabilizing for an infinite-dimensional system. We address the question of whether the sampled-data controller obtained by applying...
George Avalos, Richard Rebarber, Irena Lasiecka
We consider two problems in boundary controllability of coupled wave/Kirchoff systems. Let Ω be a bounded region in R n, n ≥ 2, with Lipschitz continuous boundary Γ. In the motivating structural...
Non-robustness of closed-loop stability for infinitedimensional systems under sample and hold (2002)
Richard Rebarber, Stuart Townley
Abstract—It is a well-known principle, for finite-dimensional systems, that applying sampled-and-hold in the feedback loop around a stabilizing state feedback (or dynamic) controller results in a...
Lack of Time-Delay Robustness for Stabilization of a Structural Acoustics Model (1999)
Avalos, George, Lasiecka, Irena, Rebarber, Richard
In this paper we consider a natural robustness question for a model for structural acoustics. This model, which has been of great interest in recent years, is represented by a wave equation in R^2...
George Avalos, Irena Lasiecka, Richard Rebarber
We consider a controlled and observed partial differential equation (PDE) which describes a structural acoustics interaction. Physically, this PDE describes an acoustic chamber with a flexible...
Lack Of Time-Delay Robustness For Stabilization Of A Structural Acoustics Model (1999)
George Avalos, Irena Lasiecka, Richard Rebarber
. In this paper we consider a natural robustness question for a model for structural acoustics. This model, which has been of great interest in recent years, is represented by a wave equation in R 2...
Canonical Forms in the Control of DPS. (1998)
Control canonical forms play an important role in the analysis of finite-dimensional problems in control theory. The goal of this research was to extend these results and develop control canonical...
Feedback Control in Distributed Parameter Systems. (1998)
In this project questions related to stabilization of vibrating system by feedback were studied. A vibrating system is uniformly stabilized by a feedback if there is a uniform rate of decay for all...
Hartmut Logemann, Claverton Down, Bath Ba Ay, Richard Rebarber
: It has been observed that for many stable feedback systems, the introduction of arbitrarily small time delays into the loop causes instability. In this paper we present a systematic treatment of...
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Well-posedness of a Structural Acoustics Control Model with Point Observation of the Pressure
George Avalos, Irena Lasiecka, Richard Rebarber
We consider a controlled and observed partial differential equation (PDE) which describes a structural acoustics interaction. Physically, this PDE describes an acoustic chamber with a flexible...