Title :
Characterizations of Input-to-State Stability for Systems With Multiple Invariant Sets
Author :
Angeli, David ; Efimov, Denis
Author_Institution :
Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
Abstract :
We generalize the theory of Input-to-State Stability (ISS) and of its characterizations by means of Lyapunov dissipation inequalities to the study of systems admitting invariant sets, which are not necessarily stable in the sense of Lyapunov but admit a suitable hierarchical decomposition. It is the latter which allows to greatly extend the class of systems to which ISS theory can be applied, allowing in a unified treatment to deal with oscillators in Euclidean coordinates, almost globally asymptotically stable systems on manifolds, systems with multiple equilibria in Rn just to name a few.
Keywords :
Lyapunov methods; asymptotic stability; nonlinear control systems; oscillators; Euclidean coordinate; ISS theory; Lyapunov dissipation inequality; asymptotically stable system; input-to-state stability; multiple invariant set; oscillators; Asymptotic stability; Lyapunov methods; Manifolds; Nickel; Stability criteria; Standards; Input-to-state stability (ISS); Lyapunov functions;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2015.2418676