Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control

By Wassim M. Haddad, V. Chellaboina, Sergey G. Nersesov. 2006

591 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/95a5081eb532d5297721f4c976de95dedd998b02

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In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Stabilization of Delay Systems: Delay-Dependent Impulsive Control (2017, unknown): “Let t,t0 denotes the flow x(t, t0, ⋅) : R → R n of (1)-(2) for a given t ∈ R+, see [32].”
Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance (2010, background): “In the analysis of passivity and Lp stability these concepts are exploited for various classes of systems in, for instance, [4], [19], [49], [53].”
Dynamic analysis of Michaelis–Menten chemostat-type competition models with time delay and pulse in a polluted environment (2009, background): “Systems with sudden perturbations lead to impulsive differential equations, which have been studied intensively and systematically in [18–28].”
Models, feedback control, and open problems of 3D bipedal robotic walking (2014, background): “Other useful notions of a solution can be found in [41, 224, 64, 49, 107].”
Recent developments on the stability of systems with aperiodic sampling: An overview (2017, background): “The stability of equilibria for the impulsive systems of the form (37) can be ensured by the existence of candidate Lyapunov functions that depend both on the system state and on time, and evolve in a discontinuous manner at impulse instants (Bainov & Simeonov, 1993; Haddad et al., 2014; Naghshtabri”
An introduction to event-triggered and self-triggered control (2012, unknown): “In this section, we reformulate the event-triggered control system as an impulsive system, e.g. , [46], [47], of the form where ¯ x ∈ X ⊆ R n x denotes the state of the system and w ∈ R n w an external disturbance.”
Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics (2014, background): “Hybrid systems and zero dynamics Consider a hybrid control system of the form of a system with impulse effects [6], [55], [20]”
Event‐triggered adaptive backstepping control for parametric strict‐feedback nonlinear systems (2018, unknown): “żi = zi+1 − kizi + θ̃i φi(xi) + kiei + θ̂ T i ( φi(xi) − φi(x̂i) ) (31) żn = −knzn + θ̃nφn(xn) + knen + θ̂ T n ( φn(xn) − φn(x̂n) ) .”
Lyapunov conditions for input-to-state stability of impulsive systems (2008, unknown): “Stability properties of such systems have been extensively investigated in the literature; see, e.g., Bainov and Simeonov (1989), Haddad, Chellaboina, and Nersesov (2006) and Tao (2001).”