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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Robust Verification and Identification of Piecewise Affine Systems
TL;DR: In this article, a verification method for piecewise affine systems is presented, where bounds on the allowed model errors are given along with the verification, and a combination of the mixed-integer programming approach and a local minimisation approach is also investigated.
Proceedings ArticleDOI
A switching anti-windup design using multiple Lyapunov functions
Liang Lu,Zongli Lin +1 more
TL;DR: This paper proposes a switching anti-windup design, which aims to enlarge the domain of attraction of the closed-loop system and allows the union of the level sets of the multiple Lyapunov functions to be contractively invariant and within thedomain of attraction.
Book ChapterDOI
Anytime Control Algorithms for Embedded Real-Time Systems
TL;DR: This paper provides a procedure for the design of controllers which, together with a conditioning process of the stochastic scheduling, provides better performance than prevailing worst case-based design, while guaranteeing almost sure stability of the resulting switching system.
Posted Content
Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers
TL;DR: The estimated output reachable set can be estimated iteratively for a given finite-time interval and the safety verification for piecewise linear systems with neural network controllers can be performed by checking the existence of intersections of unsafe regions and output reach set.
Journal ArticleDOI
Stability of discontinuous retarded functional differential equations with applications
TL;DR: Lyapunov stability results are presented and the applicability of these results are demonstrated in the analysis of several specific important classes of DDS determined by functional differential equations and differential-difference equations.
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.