A polynomial blossoming approach to stabilization of periodic time-varying systems

This paper proposes a novel polynomial blossoming approach to designing stabilizing controller for a class of periodic time-varying systems. Utilizing multi-convexity of a non-homogeneous symmetric matrix polynomial, the approach can provide a series of convex optimization conditions to guarantee the negativity/positivity of matrix polynomial. Special cases of the proposed approach are also discussed, giving the conclusion that our approach generalizes two existing matrix polynomial approaches. For periodic systems formulated with [0,1]-bounded time-varying coefficients, the designed stabilizing controller not only involves user-selectable varying gains over time intervals that are possibly non-identical to the system fundamental period, but can also guarantee the exponential stability of the closed-loop system. The effectiveness of our approach is validated and illustrated through two application-oriented simulation examples.