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
More filters
Journal ArticleDOI
Convex necessary and sufficient stabilisability conditions in switched linear systems with rank-one modes
TL;DR: A novel convex necessary and sufficient condition for state-feedback exponential stabilisability in discrete-time switched linear systems, whose modes are described by rank-one matrices, is reported and proved in the present communication.
Proceedings ArticleDOI
An Extension of Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems
TL;DR: It is shown that if the subsystem matrices commute each other, or if they are symmetric, then a common Lyapunov function exists for the two subsystems and that the switched system is exponentially stable under arbitrary switching.
Journal ArticleDOI
Overview of the recent research progress for stability and control on random nonlinear systems
TL;DR: In this paper , the fundamental and general framework of stability analysis for RNSs developed in (Wu, Apr., 2015) is revisited first, and the existing results on this subject are addressed from the perspectives of stabilisation analysis and control design as detailed as possible based on the framework mentioned above.
Proceedings ArticleDOI
Stabilizing hybrid switched motion control systems with an on-line trajectory generator
Torsten Kröger,Friedrich M. Wahl +1 more
TL;DR: Real-world experimental results achieved with a six-joint industrial manipulator are presented in order to demonstrate the potential and the high practical relevance of the idea of a universal method for stabilizing discrete-time hybrid switched-control systems of robot manipulators.
Proceedings ArticleDOI
Dynamic Controller of Switched Linear Systems : a Common Lyapunov Function Approach
TL;DR: A sufficient condition is formulated as an LMI problem for the switched controller design under arbitrary switching, a stabilizing switched controller with regional pole placements is also formulated as a convex problem, and an L MI approach is used to derive the switched dynamic controller with performance limitations.
References
More filters
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.