Hyperexponential and Fixed-Time Stability of Time-Delay Systems: Lyapunov–Razumikhin Method
Artem N. Nekhoroshikh, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti, Igor B. Furtat
Abstract
Razumikhin-like theorems on hyperexponential and fixed-time stability of time-delay systems are proposed for both explicitly and implicitly defined Lyapunov functions. While the former method is useful for stability analysis, the latter approach is more suitable for control synthesis. Examples of systems that can be stabilized hyperexponentially and in fixed time are given. The control parameters tuning algorithm is presented in the form of linear matrix inequalities. The numerical simulations illustrate the theoretical results.
Topics & Concepts
Control theory (sociology)Stability (learning theory)Lyapunov functionMathematicsLyapunov equationControl (management)Computer scienceNonlinear systemMachine learningQuantum mechanicsArtificial intelligencePhysicsStability and Control of Uncertain SystemsQuantum chaos and dynamical systemsControl and Stability of Dynamical Systems