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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Journal ArticleDOI
Delay-dependent fault detection for switched linear systems with time-varying delays-the average dwell time approach
Dan Zhang,Li Yu,Wen-An Zhang +2 more
TL;DR: A novel delay-dependent sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities (LMIs) by using a newly constructed Lyapunov functional and the average dwell time scheme.
Proceedings ArticleDOI
Stabilization and performance analysis for a class of switched systems
TL;DR: A generalized sufficient LMI condition is obtained which guarantees a /spl gamma/-performance of the closed-loop switched systems subject to input disturbances, and two performance measures being considered are the decay rate and the input-output performance.
Journal ArticleDOI
Event-triggered control for continuous-time switched linear systems
Weiming Xiang,Taylor T. Johnson +1 more
TL;DR: Three equivalent sufficient conditions are proposed to ensure the asymptotic stability of switched systems and one condition has a promising feature of affineness in system matrices, and it is extended to robust sampling case and ℒ 2 -gain analysis.
Journal ArticleDOI
Analysis and control of switched linear systems via dwell-time min-switching
Chang Duan,Fen Wu +1 more
TL;DR: A mixed time-driven and state-dependent switching strategy is proposed that guarantees an average dwell time even when all subsystems are unstable and could refrain frequent switches commonly observed in min-switching based designs.
Journal ArticleDOI
Coordinating feedback and switching for control of hybrid nonlinear processes
TL;DR: In this paper, a robust hybrid control strategy for a broad class of hybrid nonlinear processes with actuator constraints and uncertain dynamics is proposed, which is predicated on the idea of coordinating the hierarchical tasks of lower-level feedback-controller synthesis and upper-level switching logic design.
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.