A characterization of integral input-to-state stability

By David Angeli, Eduardo Sontag, Yuan Wang. IEEE Transactions on Automatic Control, 2000

687 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/6d35e5b2395b5146903e9bb1ad77581ed8563076

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In Control and Systems Engineering

Citations in the corpus

Input to State Stability: Basic Concepts and Results (2008, methodology): “and note ([11]) the following passivity-type estimate: d dt V (q(t), q̇(t)) ≤ −c1|q̇(t)|(2) + c2 |u(t)|(2) for sufficiently smallc1 > 0 and largec2 > 0.”
Stability Analysis of Nonlinear Time-Varying Systems by Lyapunov Functions with Indefinite Derivatives (2015, neutral): “(7) in [1]) |x (t)| ≤ σ (|x (t0)| , t− t0) + γ1 ( ∫ t t0 γ2 (|u (s)|) ds )”
Nonlinear norm-observability notions and stability of switched systems (2005, methodology): “Motivated by the integral versions of ISS and OSS (see [4]), we can modify the definitions by replacing supremum norms on the outputs with integral norms.”
A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems (2006, background): “By the same reasoning of the proof of 2 ⇒ 1 in Theorem 1 in [1] and by the results there concerning nonlinear delay free systems, it follows, taking into account the hypothesis (Hp1), that there exists a KL function such that, for all t ∈ [0, b), 0 < b + ∞, where the solution exists, V (xt ) (V ( 0)”
Lyapunov conditions for input-to-state stability of impulsive systems (2008, background): “This is a relatively straightforward extension of the proof of the corresponding result for continuous systems given in [2].”
A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models (2004, neutral): “F (x, u) =    1 if x < 0 10 if x > 0 [1, 10] if x = 0 (73)”
Characterizations of integral input-to-state stability for bilinear systems in infinite dimensions (2014, background): “In [3] a Lyapunov type necessary and sufficient condition for an ODE system to be iISS has been proved.”
Separable Lyapunov functions for monotone systems: Constructions and limitations. (2015, background): “In fact, it is known that ISS implies iISS (and proved in [40, 2]).”