For random diffeomorphisms depending on a parameter, nearly invariant sets are described via an associated deterministic control system. Conditions are provided guaranteeing that the system leaves the support of an invariant measure under small perturbations of the parameter and estimates for the exit times are given.

A method is proposed to fit parameters of Power System Stabilizer controllers in electromechanical multimachine power systems. The use of the Non-dominated Sorting Genetic Algorithm II heuristic method and Tabu search is considered to be initial search criteria. These methods give an approximation of the values that define the controllers. Then, the stochastic approach was used to evaluate the behavior of the parameters found when considering the system’s response to the presence of random and self-sustained in-time disturbances that affect the response of the system under steady state. The stochastic approach allows the evaluation of the system’s response through the calculation of the cost of energy loss under steady state. The method is applied to two systems: a three-machine nine-busbar system, and the Interconnected System of the Greater North (Sistema Interconectado del Norte Grande) in Chile. For these systems, the proposed methodology effectively optimized the controllers and Tabu search was shown to have a better performance than the Non-dominated Sorting Genetic Algorithm II.

This paper presents a methodology to represent ocean wave power generation based on real data observation for significant wave height (SWH or $H_s$ ) and wave period (WP or T). This technique is based on a hybrid model, which considers Fourier series and stochastic differential equations, allowing a continuous time representation of the random changes in the parameters associated with wave power generation ( $H_s$ and T). The methodology is explained, including estimation methods and a validation procedure. The data series generated by the models erre used to create simulated wave power output applying a transformed matrix and a theoretical model. The results validate the utilization of this technique, when the objective is to obtain a robust dynamic representation of a random process, oriented to linear studies.

This paper considers nonlinear stochastic systems subject to random Markovian perturbations as the size of the perturbations increases. At an operating point of the system, its exponential stability can be assessed via the Lyapunov exponents. We define an index, the stability radius, which uses the Lyapunov exponents to determine the optimal system parameters for stabilization so that the system can withstand perturbations of maximal magnitude