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
Proceedings ArticleDOI
Synthesis of Switched Linear Systems handling Sliding Motions
TL;DR: In this article, the synthesis problem on how to select the linear vector fields among the possible ones such that a switched system becomes (exponentially) stable is treated, and the design procedure allowing sliding motions to occur by introducing additional conditions is extended.
Journal ArticleDOI
Delay-dependent H∞ performance analysis and filtering for Markovian jump systems with interval time-varying delays
Xudong Zhao,Qingshuang Zeng +1 more
TL;DR: In this article, a delay-range-dependent H∞ performance condition for Markovian jump systems is proposed by constructing a different Lyapunov-Krasovskii functional.
Journal ArticleDOI
Curve Tracking Control for Autonomous Vehicles with Rigidly Mounted Range Sensors
TL;DR: This paper considers a vehicle that has a group of rays around two center rays that are perpendicular to the velocity of the vehicle and derives a hybrid strategy of switching between control laws when the vehicle gets close to singularities.
Journal ArticleDOI
Stability and Persistent Excitation in Signal Sets
TL;DR: A novel concept: M-pair, which aims at simplifying the checking of the PE condition, is introduced and it is shown that a nonlinear time-varying switched system with arbitrary switching can be shown to be UGAS without using a common Lyapunov function.
Journal ArticleDOI
Bounds and invariant sets for a class of switching systems with delayed-state-dependent perturbations
Hernan Haimovich,Maria M. Seron +1 more
TL;DR: A novel method to compute componentwise transient bounds, componentwise ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state.
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.