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
Exponential H∞ Filtering for Discrete-Time Switched State-Delay Systems Under Asynchronous Switching
Yan Zheng,Gang Feng,Jianbin Qiu +2 more
TL;DR: In this paper, the authors considered the exponential H∞ filtering problem of discrete-time switched state-delay systems under asynchronous switching and designed a full-order or reduced-order switched filter guaranteeing the exponential stability with the weighted H ∞ performance.
Journal ArticleDOI
Robust H ∞ static output feedback control of discrete-time switched polytopic linear systems with average dwell-time
TL;DR: This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties and shows that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software.
Journal ArticleDOI
Generalized Hopf bifurcation in a class of planar switched systems
Song-Mei Huan,Xiao-Song Yang +1 more
TL;DR: In this article, a generalized Hopf bifurcation in a class of planar switched systems with the phase portraits of the subsystems being locally those of similarly oriented foci at the origin is analyzed.
Journal ArticleDOI
Output feedback stabilization for planar switched nonlinear systems with asymmetric output constraints
Xueling Li,Xiangze Lin,Yun Zou +2 more
TL;DR: The method proposed in this paper is a unified tool because it works not only for switched nonlinear systems with asymmetric or symmetric output constrains but also for those without output constraints.
Journal ArticleDOI
Brief paper: A duality-based convex optimization approach to L2 -gain control of piecewise affine slab differential inclusions
Behzad Samadi,Luis Rodrigues +1 more
TL;DR: The dual parameter set of a piecewise affine (PWA) system is introduced to enable a convex formulation of PWA controller synthesis for PWA slab differential inclusions using a new convex relaxation.
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.