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We generalize and unify a range of recent results in quantized control systems (QCS) and networked control systems (NCS) literature and provide a unified framework for controller design for control systems with quantization and time scheduling via an emulation-like approach. A crucial step in our proofs is finding an appropriate Lyapunov function for the quantization/ time-schednling protocol which verifies its uniform global exponential stability (UGES). We construct Lyapunov functions for several representative protocols that are commonly found in the literature, as well as some new protocols not considered previously. Our approach is flexible and amenable to further extensions which are briefly discussed. Index Terms--Networked control systems (NCS), quantized control systems (QCS).

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work. Index Terms--Disturbances, hybrid control, input-to-state stability (ISS), quantized feedback.

The purpose of this note is to demonstrate that a unified study of quantization and delay effects in nonlinear control systems is possible by merging the quantized feedback control methodology recently developed by the author and the small-gain approach to the analysis of functional differential equations with disturbances proposed earlier by Teel. We prove that under the action of a robustly stabilizing feedback controller in the presence of quantization and time delays satisfying suitable conditions, solutions of the closed-loop system starting in a given region remain bounded and eventually enter a smaller region. We present several versions of this result and show how it enables global asymptotic stabilization via a dynamic quantization strategy. Index Terms--Input-to-state stability, nonlinear system, quantized control, small-gain condition, time delays.

This paper studies state quantization schemes for feedback stabilization of control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given information constraint. We explore several ways of measuring the destabilizing effect of a quantizer on the closed-loop system, including (but not limited to) the worst-case quantization error. In each case, we show how quantizer design can be naturally reduced to a version of the so-called multicenter problem from locational optimization. Algorithms for obtaining solutions to such problems, all in terms of suitable Voronoi quantizers, are discussed. In particular, an iterative solver is developed for a novel weighted multicenter problem which most accurately represents the least destabilizing quantizer design. A simulation study is also presented. Index Terms--Feedback stabilization, locational optimization, quantized control.

This paper proposes several definitions of "norm-observability" for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for norm-observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems. Index Terms--LaSalle's stability theorem, nonlinear system, observability, switched system.

This note is concerned with the problem of finding a quadratic common Lyapunov function for a large family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families. Index Terms--Common Lyapunov functions, gradient algorithms, randomized algorithms, switched linear systems.

We consider the problem of stabilizing a linear time-invariant system using sampled encoded measurements of its state or output. We derive a relationship between the number of values taken by the encoder and the norm of the transition matrix of the open-loop system over one sampling period, which guarantees that global asymptotic stabilization can be achieved. A coding scheme and a stabilizing control strategy are described explicitly. Index Terms--Asymptotic stabilization, coding, limited information, linear system, sampling.

This paper introduces and studies the notion of output--input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output--input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the "input-to-state stability" (ISS) philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of output--input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control. Index Terms--Adaptive control, asymptotic stabilization, detectability, input-to-state stability (ISS), minimum phase, nonlinear system, relative degree.