A Lyapunov approach to incremental stability properties

By David Angeli. IEEE Transactions on Automatic Control, 2002

793 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/1676442b42504ba4ea1052742782e043f643bba3

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In Control and Systems Engineering

Citations in the corpus

Synchronization in complex networks of phase oscillators: A survey (2014, background): “Indeed, the coupled oscillator model (1) can be regarded as an exponentially stable system subject to the disturbance ω ∈ 1⊥n and synchronization can be studied using classic control-theoretical concepts such as input-to-state stability, practical stability, ultimate boundedness (Khalil, 2002) or th”
Cyber–Physical Systems: A Perspective at the Centennial (2012, background): “Concerning an approximate bisimulation relation, if a nonlinear control system is incrementally asymptotically stable [113], then it is -approximately bisimilar [114] to a symbolic model of the original continuous system that can be constructed by aggregating states and control inputs using several ”
Incremental quadratic stability (2013, background): “Considering a time-invariant δQS system described by ẋ = F̄ (x,w) (3) we can make the following conclusions using the results in [4, 16, 26, 27, 12].”
Convergent systems : analysis and synthesis (2005, background): “Key words: Convergent systems, stability properties, asymptotic properties, interconnected systems, observers, output-feedback”
Approximately bisimilar symbolic models for nonlinear control systems (2007, background): “Given a control system Σ, any τ ∈ R+, η ∈ R+ and µ ∈ R+, define the following transition system: (5.1) Tτ,η,µ(Σ) := (Q2, L2, 2 - , O2, H2), where: • Q2 = [Rn]η; • L2 = [L1]µ; • q l 2 - p, if ‖p− x(τ, q, l)‖ ≤ η/2; • O2 = Rn; • H2 = ı : Q2 ↪→ O2.”
Input to State Stability: Basic Concepts and Results (2008, methodology): “A sufficient condition for i-ISS in dissipation terms, using a similar idea, was given in [4].”
Partial synchronization: from symmetry towards stability (2002, methodology): “In [41] a bit stronger notion was called incremental global asymptotic stability(δGAS); therein the necessary and sufficient conditions for δGAS were formulated in terms of the existence of Lyapunov functions.”
Review on computational methods for Lyapunov functions (2015, background): “Incremental stability was studied in Lohmiller and Slotine 1998 [156] and Angeli 2002 [10].”
Analysis of Interconnected Oscillators by Dissipativity Theory (2007, neutral): “Remark 5: The global exponential stability result of (Π ⊗ Ip)X = 0 may also be viewed as an incremental inputto-state stability ( δ-ISS) property of the network with S∆ being the correspondingδ-ISS Lyapunov function (see [34]).”
Convergent dynamics, a tribute to Boris Pavlovich Demidovich (2004, methodology): “Several papers studying such stability properties in their own respect appeared [6] [11] [1] [8].”
A Differential Lyapunov Framework for Contraction Analysis (2012, methodology): “The incremental Lyapunov approach proposed in [3], establishes incremental stability by checking a pointwise geometric condition in the product space .”
Contraction methods for nonlinear systems: A brief introduction and some open problems (2014, background): “We remark that contractivity can also be thought of as a very strong form of incremental stability [25].”
Monotone control systems (2002, methodology): “Observe that the definition of monotonicity amounts to the requirement that: for each ξ ∈ Γ, and each u ∈ U [2] ∞ , the solution φ(t, ξ, u) of (15) with initial condition x(0) = ξ belongs to Γ for all t ≥ 0 (forward invariance of Γ with respect to (15)).”
Nonlinear norm-observability notions and stability of switched systems (2005, neutral): “h(x) = 0 if x ∈ [0, 1], h(x) ∈ [0, 2] if x ∈ [1, 2], h(x) = x if x ≥ 2”