Hybrid systems: Generalized solutions and robust stability

By Rafal K. Goebel, João Pedra Hespanha, Andrew R. Teel, Chaohong Cai, Ricardo G. Sanfelice. 2004

216 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/2972e667a7aede1b17cdf282916f516bea0f8827

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In Control and Systems Engineering

Citations in the corpus

Characterizations of input-to-state stability for hybrid systems (2009, background): “A solution of a hybrid system is a function, defined on a hybrid time domain, that can flow in continuous time and also jump at discrete instants [6].”
Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability (2007, methodology): “The other aspect of the " set-valuedness " of the systems we consider, the set-valued data, serves as an analytical tool to capture nonuniqueness of solutions and is also deeply motivated by the questions of robustness, as outlined in [9].”
Stability analysis for stochastic hybrid systems: A survey (2014, methodology): “For non-stochastic hybrid systems, weak regularity conditions, as found inGoebel, Hespanha, Teel, Cai, and Sanfelice (2004), Goebel et al. (2009), Goebel et al. (2012, Ch. 7), or Goebel and Teel (2006), are sufficient for Lyapunov stability plus global attractivity to imply uniform Lagrange stabilit”
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms (2009, unknown): “(2003), Goebel et al. (2004), and Sanfelice et al. (2007). Many methods are currently available (Mehaute et al.”
Unicycle Coverage Control Via Hybrid Modeling (2010, methodology): “More recently, [12], [13] revisits the notion of hybrid (time) trajectories and develops an invariance principle based on graphical convergence of set-valued maps.”
Solutions to hybrid inclusions via set and graphical convergence with stability theory applications (2006, methodology): “Most recently, the concurrent conference papers by Collins [9] and the authors et al. [ 11 ] have proposed treating the number of jumps as an independent variable and parameterizing the state of a hybrid system by (t; j) { that is, x(t; j) is the state at time t and after j jumps.”
Analytical and numerical Lyapunov functions for SISO linear control systems with first‐order reset elements (2011, methodology): “To avoid this nonconverging Zeno behavior and allow to establish useful exponential stability properties of the FORE control system, (see, [13, 15]), the overall closed-loop system is augmented with a temporal regularization namely with a timer ensuring that between two consecutive resets (or jumps)”
On the Observability of Nonlinear and Switched Systems (2009, unknown): “For switched systems, the concept of observability and methods of observer design are strongly related to the dwell time and the sequence of switching, thus it is important to recall (in our context) the following definition of hybrid time trajectory [18] (see also [13]).”