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
An exact stability test for planar and multi-modal piecewise linear systems
Yasushi Iwatani,Shinji Hara +1 more
TL;DR: In this article, a necessary and sufficient stability condition for planar and multimodal piecewise linear systems is derived in terms of poles and zeros of subsystems, and it is computationally tractable.
Proceedings ArticleDOI
Finite-time stability and finite-time boundedness for switched systems with sector bounded nonlinearities
TL;DR: In this article, the authors studied finite-time stability and boundedness of switched systems with sector bounded nonlinearities and provided sufficient conditions that the switched nonlinear systems are stable or bounded.
Journal ArticleDOI
Finite-Time Boundedness and Control for Affine Switched Systems
Han Lu,Cunyong Qiu,Lin Jiang +2 more
TL;DR: The problems of finite-time boundedness (FTB) analysis and stabilization are addressed for affine switched systems, and several definitions and sufficient conditions are proposed to study FTB and H∞ performance.
Journal ArticleDOI
Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint
TL;DR: In this article, the state estimation problem for a class of switched linear systems which only switches in some short interval is addressed and optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances.
Journal ArticleDOI
Stability Verification for a Class of Stochastic Hybrid Systems by Semidefinite Programming
Kairong Liu,Meilun Li,Zhikun She +2 more
TL;DR: In this paper, the analysis and verification of stability for a class of stochastic hybrid systems (SHSs), which contain not only continuous flows described by Stochastic differential flow, but also continuous flows with stochastically varying stochas.
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.