Discontinuous dynamical systems

By Jorge Cortés. IEEE Control Systems, 2008

1,104 citations recorded by the source corpus.

This article has presented an introductory tutorial on discontinuous dynamical systems. Various examples illustrate the pertinence of the continuity and Lipschitzness properties that guarantee the existence and uniqueness of classical solutions to ordinary differential equations. The lack of these properties in examples drawn from various disciplines motivates the need for more general notions than the classical one. First, we introduced notions of solution for discontinuous systems. Second, we reviewed the available tools from non- smooth analysis to study the gradient information of candidate Lyapunov functions. And, third, we presented nonsmooth stability tools to characterize the asymptotic behavior of solutions.

Subfields: Aerospace Engineering, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/45d02dce688e575868ab057ad36019e06cf174d8

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In Aerospace Engineering

In Control and Systems Engineering

Citations in the corpus

Continuous and discontinuous opinion dynamics with bounded confidence (2012, methodology): “We give the definitions of classical, Carathéodory and Krasovskii solutions (see [12, 9]).”
Distributed Continuous-Time Convex Optimization With Time-Varying Cost Functions (2015, background): “Thus, the solution should be investigated in terms of differential inclusions by using nonsmooth analysis [30], [31].”
Distributed Tracking Control for Linear Multiagent Systems With a Leader of Bounded Unknown Input (2013, background): “The readers can refer to [22], [23] and references therein for further applications of nonsmooth analysis in the area of multiagent systems.”
Distributed Adaptive Control of Synchronization in Complex Networks (2012, background): “Assumption 1 is the so-called QUAD condition (or one-sided Lipschitz) on vector fields [31], [32].”
Unknown input observer design for one-sided Lipschitz nonlinear systems (2015, background): “Remark 1 Every vector function that is locally Lipschitz satisfies the one-sided Lipschitz condition, but the converse is not true [36].”
Nonsmooth Barrier Functions With Applications to Multi-Robot Systems (2017, background): “forward invariance in other work (see [19]).”
A Lyapunov approach to second-order sliding mode controllers and observers (2008, background): “Remark 1: Since V (x) (2) is continuous but not differentiable, a nonsmooth version of Lyapunov’s theory is required (see [5], and the recent tutorial paper [ 6 ] for an overview).”
Finite-Time Consensus for Switching Network Topologies with Disturbances (2013, background): “The reader is referred to [21] for a comprehensive account of the notions of solution for discontinuous dynamical systems.”