Stability and robustness analysis of a linear time-periodic system subjected to random perturbations

In this work, new methods of guaranteeing the stability of linear time periodic dynamical systems with stochastic perturbations are presented. In the approaches presented here, the Lyapunov–Floquet (L–F) transformation is applied first so that the linear time-periodic part of the equations becomes time-invariant. For the linear time periodic system with stochastic perturbations, a stability theorem and related corollary have been suggested using the results previously obtained by Infante. This technique is not only applicable to systems with stochastic parameters but also to systems with deterministic variation in parameters. Some illustrative examples are presented to show the practical applications. These methods can be used to investigate the degree of robustness and design controllers for systems with time periodic coefficients subjected to random perturbations.

► We present new methods of guaranteeing the stability of linear time periodic dynamical systems with stochastic perturbations. ► We use the Lyapunov–Floquet (L–F) transformation to convert linear time periodic system into a time invariant one. ► Stability bounds on the stochastic variations are obtained using Lyapunov type approach.