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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.

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Citations
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Journal ArticleDOI

Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach

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

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.
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