Hybrid dynamical systems

@article{Goebel2009HybridDS,
  title={Hybrid dynamical systems},
  author={Rafal Goebel and Ricardo G. Sanfelice and Andrew R. Teel},
  journal={IEEE Control Systems},
  year={2009},
  volume={29},
  pages={28-93}
}
Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data… 
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References

SHOWING 1-10 OF 133 REFERENCES
Perspectives and results on the stability and stabilizability of hybrid systems
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
GENERALIZED SOLUTIONS TO HYBRID DYNAMICAL SYSTEMS
TLDR
This paper shows that generalized solutions to a hybrid system are exactly the solutions that arise when measurement noise in the system is taken into account.
Basic problems in stability and design of switched systems
By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments
Smooth Lyapunov Functions for Hybrid Systems—Part I: Existence Is Equivalent to Robustness
TLDR
The equivalence between the robustness of stability with respect to two measures and a characterization of such stability in terms of a smooth Lyapunov function is established.
Stability theory for hybrid dynamical systems
  • H. Ye, A. Michel, L. Hou
  • Mathematics
    Proceedings of 1995 34th IEEE Conference on Decision and Control
  • 1995
Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior in different parts of a system are of great current interest. In the present paper we first formulate a
Hybrid Systems: Limit Sets and Zero Dynamics with a View Toward Output Regulation
Summary. We present results on omega-limit sets and minimum phase zero dynamics for hybrid dynamical systems. Moreover, we give pointers to how these results may be useful in the future for solving
Supervising a family of hybrid controllers for robust global asymptotic stabilization
TLDR
This paper describes an algorithm for achieving robust, global asymptotic stabilization in nonlinear control systems by supervising the actions of a family of hybrid controllers, using the concept of "events" for hybrid systems.
A Trajectory-Space Approach to Hybrid Systems
We develop a framework for studying dynamical properties of hybrid systems based on considering the space of all possible trajectories of the system. In this way it is possible to treat both
Recent trends in the stability analysis of hybrid dynamical systems
Dramatic progress in computing capabilities has resulted in the synthesis and implementation of increasingly complex dynamical systems. Since such systems frequently exhibit simultaneously several
...
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