Passivity gains and the ``secant condition for stability

DOI10.1016/j.sysconle.2005.06.010zbMath1129.93476arXivmath/0503117OpenAlexW1982622986MaRDI QIDQ2504646

Eduardo D. Sontag

Publication date: 25 September 2006

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503117

zbMATH Keywords

stabilitynegative feedbackpassive systemssecant condition

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Popov-type stability of feedback systems (93D10) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Input-output approaches in control theory (93D25)

Related Items (11)

A rolled-off passivity theorem ⋮ Time‐optimal control of piecewise affine bistable gene‐regulatory networks ⋮ Stability and Robustness Analysis of a Class of Cyclic Biological Systems ⋮ Secant and Popov-like conditions in power network stability ⋮ Diagonal stability of a class of cyclic systems and its connection with the secant criterion ⋮ Effect of model selection on prediction of periodic behavior in gene regulatory networks ⋮ Robust stability analysis of gene-protein regulatory networks with cyclic activation-repression interconnections ⋮ Passivity-based Stability of Interconnection Structures ⋮ Discrete and ultradiscrete models for biological rhythms comprising a simple negative feedback loop ⋮ Diagonal stability of matrices with cyclic structure and the secant condition ⋮ Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities

Cites Work

• The Poincaré-Bendixson theorem for monotone cyclic feedback systems
• The secant condition for instability in biochemical feedback control. I: The role of cooperativity and saturability
• Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback
• L\(_2\) gain and passivity techniques in nonlinear control.
• Diagonal stability of a class of cyclic systems and its connection with the secant criterion
• <tex>L_infty</tex>-stability criteria for interconnected systems using exponential weighting
• System analysis via integral quadratic constraints
• Causality in Hilbert Space
• Meagre functions and asymptotic behaviour of dynamical systems
• Stabilization of positive linear systems
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