Lyapunov Stability
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the notion of Lyapunov stability occurs in the study of dynamical systems. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point xe stay near xe forever, then xe is Lyapunov stable. More strongly, if xe is Lyapunov stable and all solutions that start out near xe converge to xe, then xe is asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how q...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the notion of Lyapunov stability occurs in the study of dynamical systems. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point xe stay near xe forever, then xe is Lyapunov stable. More strongly, if xe is Lyapunov stable and all solutions that start out near xe converge to xe, then xe is asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs.
