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A Unified Lyapunov Approach to Analysis of Oscillations and Stability for Systems With Piecewise Linear Elements

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3 Author(s)
Tingshu Hu ; Dept. of Electr. & Comput. Eng., Univ. of Massachusetts, Lowell, MA, USA ; Thibodeau, T. ; Teel, A.R.

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.

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Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 12 )