Chaouki T. Abdallah

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This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion, the knowledge gained in the decades of research into this important open problem. The paper shows that although many approaches and techniques exist to approach(More)
Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to “difficult” control problems. Unfortunately, the number of samples required in order to guarantee stringent performance levels may be prohibitively large. This paper introduces bootstrap learning methods and the concept of stopping times to(More)
In this paper we show how a number of interesting linear control system analysis and design problems can be reduced to Quantiier Elimination (QE) problems. We assume a xed structure for the compensator, with design parameters q i. The problems considered are problems that currently have no general solution. However, the problems must be of modest complexity(More)
We present a generalization of Benford's law for the first significant digit. This generalization is based on keeping two terms of the Fourier expansion of the probability density function of the data in the modular logarithmic domain. We prove that images in the discrete cosine transform domain closely follow this generalization. We use this property to(More)
A deterministic dynamic nonlinear time-delay system is developed to model load balancing in a cluster of computer nodes used for parallel computations. The model is shown to be self consistent in that the queue lengths cannot go negative and the total number of tasks in all the queues and the network are conserved (i.e., load balancing can neither create(More)
A linear time-delay system is used to model load balancing in a cluster of computer nodes used for parallel computations. The linear model is analyzed for stability in terms of the delays in the transfer of information between nodes and the gains in the load balancing algorithm. This model is compared with an experimental implementation of the algorithm on(More)
In Anderson et al. (1975) the application of Tarski–Seidenberg decision theory (Tarski, 1951, Seidenberg, 1954) for the solution of the static output feedback stabilization problem for specific problems was first proposed. The general static output feedback stabilization problem is one of the most important open problems in feedback design. The problem can(More)