Journal ArticleDOI
Quantized feedback stabilization of linear systems
TLDR
A new control design methodology is proposed, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves, which yields global asymptotic stability.Abstract:
This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear time-invariant feedback, this approach yields global asymptotic stability.read more
Citations
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Journal ArticleDOI
Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks
TL;DR: This note investigates a simple event-triggered scheduler based on the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant and shows how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.
Journal ArticleDOI
Basic problems in stability and design of switched systems
Daniel Liberzon,A.S. Morse +1 more
TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
Journal ArticleDOI
Control under communication constraints
TL;DR: This paper forms a control problem with a communication channel connecting the sensor to the controller, and provides upper and lower bounds on the channel rate required to achieve different control objectives.
Journal ArticleDOI
Stabilization of linear systems with limited information
Nicola Elia,Sanjoy K. Mitter +1 more
TL;DR: By relaxing the definition of quadratic stability, it is shown how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system.
Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
TL;DR: In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.
References
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Book
Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Journal ArticleDOI
Smooth stabilization implies coprime factorization
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.
Journal ArticleDOI
On characterizations of the input-to-state stability property
Eduardo D. Sontag,Yuan Wang +1 more
TL;DR: In this paper, the Lyapunov sufficient condition for "input-to-state stability" (ISS) is also shown to be necessary and sufficient, which is an open question raised by several authors.
Journal ArticleDOI
Supervisory control of families of linear set-point controllers - Part I. Exact matching
TL;DR: It is shown that in the absence of unmodeled process dynamics, the proposed supervisor can successfully perform its function even if process disturbances are present, provided they are bounded and constant.