Title :
A Unified Lyapunov Approach to Analysis of Oscillations and Stability for Systems With Piecewise Linear Elements
Author :
Hu, Tingshu ; Thibodeau, Thomas ; Teel, Andrew R.
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Massachusetts, Lowell, MA, USA
Abstract :
This technical note develops a unified Lyapunov approach to analysis of self-induced oscillations and stability for systems with piecewise linear elements. For self-induced oscillation within a global or regional attractor, invariant level sets of a piecewise quadratic Lyapunov function are obtained to bound the attractor via linear matrix inequality based optimization. The analysis results for self-induced oscillations are easily adapted to global or regional stability analysis.
Keywords :
Lyapunov methods; linear matrix inequalities; optimisation; oscillations; piecewise linear techniques; invariant level sets; linear matrix inequality based optimization; oscillations analysis; piecewise linear elements; regional attractor; self induced oscillations; stability analysis; unified lyapunov approach; Limit-cycles; Linear matrix inequalities; Lyapunov method; Optimization; Oscillators; Stability analysis; Trajectory; Piecewise linear systems; piecewise quadratic function; self-induced oscillation; stability;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2010.2073070
