scispace - formally typeset
Journal ArticleDOI

Perspectives and results on the stability and stabilizability of hybrid systems

TLDR
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.
Abstract
This paper introduces the concept of a hybrid system 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. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.

read more

Citations
More filters
Journal ArticleDOI

Exponential stability of impulsive systems with application to uncertain sampled-data systems

TL;DR: A positive constant is found which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed and is applied to the analysis and state-feedback stabilization of nonlinear time-varying impulsive systems.
Book ChapterDOI

Engineering Self-Adaptive Systems through Feedback Loops

TL;DR: The state-of-the-art in engineering self-adaptive systems is explored and the critical challenges the community must address to enable systematic and well-organized engineering of self- Adaptive and self-managing software systems are identified.
Journal ArticleDOI

Stability and Stabilization of Continuous-Time Switched Linear Systems

TL;DR: This paper addresses two strategies for the stabilization of continuous-time, switched linear systems and is designed from the solution of what the authors call Lyapunov-Metzler inequalities from which the stability condition (including chattering) is expressed.
Journal ArticleDOI

Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time

TL;DR: The stability and l 2-gain problems for a class of discrete-time switched systems with average dwell time (ADT) switching are investigated by allowing the Lyapunov-like functions to increase during the running time of subsystems to facilitate the studies on the issue of asynchronous control.
References
More filters
Book

Applied Nonlinear Control

TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Book

Linear Matrix Inequalities in System and Control Theory

Edwin E. Yaz
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
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.
Related Papers (5)