Stability Radii via Lyapunov Exponents for Large Stochastic Systems

Stability region and radius in electric power systems under sustained random perturbations

“…[23] uses the Lyapunov exponent to define stability radii in electric systems subjected to random perturbations self-sustained over time, using the numerical methods reported in [19]. This work shows a methodology that allows determining the maximum perturbation size that a system can resist without losing stability.…”

“…Theoretically, the stability radius of a linear stochastic system (3) is defined as r :¼ inffq P 0; kðqÞ > 0g, compare [23]. If the system depends on a parameter K 2 R n as in (15), one considers the stability radius r K :¼ inffq P 0; k K ðqÞ > 0g; for each parameter value K. Here k K ðqÞ denotes the Lyapunov exponent of the system (15) for each K. If the goal of the system design is to maximize the size of a random perturbation that the system can sustain without becoming unstable, then we are looking for…”