Stability and Robustness Analysis of Quasi-Periodic System subjected to Uncertain Parametric Excitations and Nonlinear Perturbations

Abstract

In this work, the asymptotic stability bounds are identified for a class of linear quasi-periodic dynamical systems with stochastic parametric excitations and nonlinear perturbations. The application of a Lyapunov-Perron (L-P) transformation converts the linear part of such systems to a linear time-invariant form. In the past, using the Infante approach for linear time-invariant systems, stability theorem and corollary were derived and demonstrated for time periodic systems with variation in stochastic parameters. In this work, the same is extended towards linear quasi-periodic with stochastic parameter variations. Furthermore, the Lyapunov's direct approach is employed to formulate the stability conditions for quasi-periodic system with nonlinear perturbations. If the nonlinearities satisfy a bounding condition, sufficient conditions for asymptotic stability are derived for such systems. The application of both derived stability theorems are demonstrated with practical examples of commutative and non-commutative quasi-periodic systems.