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
Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems
TL;DR: A continuous feedback controller is designed for the switched system, which guarantees that asymptotic output tracking is achieved without transgression of the constraints and all closed-loop signals remain bounded, provided that the initial states are feasible.
Journal ArticleDOI
Dynamic Output Feedback Control of Switched Linear Systems
TL;DR: A particular class of matrix inequalities, the so-called Lyapunov--Metzler inequalities, provides conditions for open-loop stability analysis and closed-loop switching control using state and output feedback and lower bounds on the cost associated with the optimal switching control strategy are derived from a feasible solution to the Hamilton--Jacobi--Bellman inequality.
Journal ArticleDOI
Asynchronous Filtering of Discrete-Time Switched Linear Systems With Average Dwell Time
TL;DR: The problem of asynchronous filtering for the underlying systems in linear cases is formulated and the conditions of the existence of admissible asynchronous filters are obtained.
Journal ArticleDOI
Quadratic stability of a class of switched nonlinear systems
Jun Zhao,Georgi M. Dimirovski +1 more
TL;DR: A necessary and sufficient condition for quadratic stability of this class of switched systems is derived by using Karush-Kuhn-Tucker condition for nonlinear programming problems.
Journal ArticleDOI
Switching LPV control of an F-16 aircraft via controller state reset
Bei Lu,Fen Wu,SungWan Kim +2 more
TL;DR: A systematic switching LPV control design method is presented to determine if it is practical to use for flight control designs over a wide angle of attack region and parameter-dependent switching logics, hysteresis switching and switching with average dwell time, are examined.
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.
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.