Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
R.A. Decarlo,Michael S. Branicky,Stefan Pettersson,Bengt Lennartson +3 more
- Vol. 88, Iss: 7, pp 1069-1082
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
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Proceedings ArticleDOI
Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation
TL;DR: In this paper, the analysis of stability for a class of switched linear systems, modeled by hybrid automata, is presented, where the dynamics are assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space.
Proceedings ArticleDOI
H ∞ and dwell time specifications of switched linear systems
Jose C. Geromel,P. Colaneri +1 more
TL;DR: This paper deals with continuous-time systems and addresses the problem of characterizing open-loop switching strategies, based on dwell time specification, assuring a pre-specified root mean square gain (RMS) at the specified H∞ level.
Proceedings ArticleDOI
On reachable set estimation for discrete-time switched linear systems under arbitrary switching
TL;DR: It can be shown that the M-step sequence method can also reduce the conservativeness in stability analysis for discrete-time switched systems under arbitrary switching in contrast to switched Lyapunov function method.
Journal ArticleDOI
Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model
Dadong Tian,Shutang Liu,Wen Wang +2 more
Journal ArticleDOI
Performance analysis and design of dynamic output feedback control for switched systems
TL;DR: Behind the stability of discrete-time switched systems, the results are focused on its performance analysis and its guaranteed cost certification, and on the design of a stabilising controller, which belongs to the class of dynamic output feedback controller minimising a guaranteed cost.
References
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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
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.
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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.