Periodic stabilization for linear time-periodic ordinary differential equations
This paper studies the periodic feedback stabilization of the controlled linear time-periodic ordinary differential equation: ẏ(t) = A(t)y(t) + B(t)u(t), t ≥ 0, where [A(·), B(·)] is a T-periodic pair, i.e., A(·) ∈ L∞(ℝ+; ℝn×n) and B(·) ∈ L∞(ℝ+; ℝn×m) satisfy respectively A(t + T) = A(t) for a.e. t ≥ 0 and B(t + T) = B(t) for a.e. t ≥ 0. Two periodic stablization criteria for a T-period pair [A(·), B(·)] are established. One is an analytic criterion which is related to the transformation over time...