Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems

Vijaysekhar Chellaboina ,Alexander Leonessa ,Wassim M Haddad

doi:10.1109/acc.1999.782317

Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems

Vijaysekhar Chellaboina , Alexander Leonessa + Show 1 more

https://doi.org/10.1109/acc.1999.782317

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Publication Date: Jan 1, 1999

Citations: 15

Affiliation: Georgia Institute of Technology

#Invariant Set Theorems #Lower Semicontinuous Lyapunov Functions + Show 8 more

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Abstract

In this paper we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems.

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