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In this paper we solve tracking and disturbance rejection problems for stable infinitedimensional systems using a simple low-gain controller suggested by the internal model principle. For stable discrete-time systems, it is shown that the application of a low-gain controller (depending on only one gain parameter) leads to a stable closed-loop system which asymptotically tracks reference signals r of the form r(k) = ∑jN=1 λjk rj, where rj ε Cp and λj ε C with ∣λj∣ ε = 1 for j = 1, … ,N. The closed-loop system also rejects disturbance signals which are asymptotically of this form. The discrete-time result is used to derive results on approximate tracking and disturbance rejection for a large class of infinite-dimensional sampled-data feedback systems, with reference signals which are finite sums of sinusoids, and disturbance signals which are asymptotic to finite sums of sinusoids. The results are given for both input-output systems and state-space systems. [ABSTRACT FROM AUTHOR]

The paper addresses both detection and stabilization problems involving communication errors and capacity constraints. Discrete-time partially observed linear systems are studied. Unlike the classic theory, the sensor signals are transmitted to the estimator/controller over a noisy digital communication link modeled as a stochastic stationary discrete memoryless channel. It is shown that for noise-free plants, the Shannon capacity of the channel constitutes the border separating the cases where stabilization and reliable detection (asymptotic state estimation) with arbitrarily large probability are and are not possible, respectively. [ABSTRACT FROM AUTHOR]

A small-gain theorem, which can be applied to a wide class of systems that includes systems satisfying the weak semigroup property, is presented in the present work. The result generalizes all existing results in the literature and exploits notions of weighted, uniform, and nonuniform input-to-output stability properties. Applications to partial state feedback stabilization problems with sampled-data feedback applied with zero order hold and positive sampling rate are also presented. [ABSTRACT FROM AUTHOR]