On stability analysis methods for large-scale discrete-time systems

• Published in: Automatica (Oxford) Vol. 55; pp. 66 - 72
• Main Authors: Gielen, Rob H., Lazar, Mircea
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-05-2015
• Subjects: Discrete-time systems; Large-scale systems; Lyapunov methods; Stability analysis; Discrete-time systems; Stability analysis; Large-scale systems; Lyapunov methods
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2015.02.034

This paper proposes a set of Lyapunov-type conditions that are suited for stability analysis of large-scale discrete-time systems. A time-wise relaxation of the Lyapunov function decrease condition is employed to derive a set of global and distributed stability conditions. Essentially, these conditions allow to make a trade-off between complexity and conservatism by extending the time-horizon over which the decrease condition should hold. It is shown that for exponentially stable dynamics and any candidate Lyapunov function, there exists a finite time for which the proposed global or distributed stability conditions hold. Hence, it is possible to use functions with a particular structure to make verification of stability scalable for large-scale systems. The developed results are applied to establish stability of a benchmark power systems example.