The exponential input-to-state stability property: characterisations and feedback connections
Chris Guiver, Hartmut Logemann
Abstract
Abstract The exponential input-to-state stability (ISS) property is considered for systems of controlled nonlinear ordinary differential equations. A characterisation of this property is provided, including in terms of a so-called exponential ISS Lyapunov function and a natural concept of linear state/input-to-state $$L^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -gain. Further, the feedback connection of two exponentially ISS systems is shown to be exponentially ISS provided a suitable small-gain condition is satisfied.
Topics & Concepts
Property (philosophy)Exponential functionExponential stabilityLyapunov functionStability (learning theory)State (computer science)Ordinary differential equationMathematicsFunction (biology)Exponential growthNonlinear systemApplied mathematicsDifferential equationComputer scienceMathematical analysisAlgorithmPhysicsMachine learningBiologyEvolutionary biologyQuantum mechanicsEpistemologyPhilosophyStability and Control of Uncertain SystemsControl and Stability of Dynamical SystemsStability and Controllability of Differential Equations