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
Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach
Ligang Wu,James Lam +1 more
TL;DR: This paper proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach, and is cast into a convex optimization problem which can be efficiently handled by using standard numerical software.
DissertationDOI
Scalable analysis of nonlinear systems using convex optimization
TL;DR: This thesis investigates how convex optimization can be used to analyze different classes of nonlinear systems at various scales algorithmically, and proposes a sum of squares methodology for the analysis of systems described by parabolic PDEs.
Journal ArticleDOI
Robust Exponential Stability and Disturbance Attenuation for Discrete-Time Switched Systems Under Arbitrary Switching
TL;DR: In this note, the global exponential stability of discrete-time switched systems under arbitrary switching is investigated and an equivalent condition which has a promising feature that is convex in system matrices is derived, leading to a robust stability criterion for uncertain discrete- time switched linear systems.
Journal ArticleDOI
How to model and prove hybrid systems with KeYmaera: a tutorial on safety
TL;DR: It is shown how the interactive features of KeYmaera can help users understand their system designs better and prove complex properties for which the automatic prover of Keymaera still takes an impractical amount of time.
Journal ArticleDOI
Quadratic stabilization of switched uncertain linear systems: a convex combination approach
TL;DR: This work proposes a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable.
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.