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
Smooth patchy control Lyapunov functions
TL;DR: It is proved that a smooth patchy control Lyapunov function exists for any asymptotically controllable nonlinear system, and a construction is shown of a stabilizing hybrid feedback that is robust to measurement noise.
Proceedings ArticleDOI
Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers
TL;DR: In this paper, a layer-by-layer approach is developed for the output reachable set computation of ReLU neural networks, which is formulated in the form of a set of manipulations for a union of polytopes.
Journal ArticleDOI
The geometry of convex cones associated with the lyapunov inequality and the common lyapunov function problem
Oliver Mason,Robert Shorten +1 more
TL;DR: In this article, the structure of several convex cones that arise in the study of Lyapunov functions is investigated, in particular the cones associated with quadratic and non-linear systems.
Proceedings ArticleDOI
Stabilization of continuous-time singularly perturbed switched systems
TL;DR: It is shown that the stability of slow and fast switched subsystems is not a sufficient condition for stability of the corresponding two-time scale switched system, under an arbitrary switching law, and LMI conditions to design a state-feedback control law stabilizing continuous-time singularly perturbed switched linear systems are proposed.
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.