Stability of linear stochastic systems via Lyapunov exponents and applications to power 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.…”

“…The work reported in [19] shows the results of analyzing the small signal stability of electric systems subjected to multiplicative stochastic perturbations through the calculation of Lyapunov exponents. Three numerical methods are shown that allow determining a single Lyapunov exponent that allows generalizing the analysis of classical deterministic eigenvalues.…”

“…[26] uses the methods reported in [19] to define performance indicators in linear stochastic systems subjected to random perturbations that are represented by a multiplicative model.…”

“…(19) gives the maximum perturbation size that the system can support when it is in the critical condition k ij % 0 for each PSS controller, using the gain values ðk 1Ã ; . .…”

Stochastic H2/H∞ control of nonlinear systems with time-delay and state-dependent noise

“…[4]. Since nonlinearity, stochasticity and time-delay are three main sources resulting in the complexities of systems in reality, a great deal of attention has been devoted to nonlinear stochastic systems with time-delay [5][6][7][8][9][10].…”