Stability conditions for impulsive dynamical systems
Sergey Dashkovskiy, В. И. Слынько
Abstract
Abstract In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.
Topics & Concepts
MathematicsDynamical systems theoryStability (learning theory)Control theory (sociology)Dynamical system (definition)Lyapunov functionState spaceApplied mathematicsDwell timeExponential stabilityWork (physics)State (computer science)Computer scienceAlgorithmNonlinear systemControl (management)PhysicsQuantum mechanicsStatisticsMachine learningThermodynamicsClinical psychologyMedicineArtificial intelligenceStability and Controllability of Differential Equationsstochastic dynamics and bifurcationNonlinear Dynamics and Pattern Formation