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This paper provides methodology for designing reduced-order controllers for large-scale, linear systems represented by differential equations having time-periodic coefficients. The linear time-periodic sys tem is first converted into a form in which the system stability matrix is time invariant. This is achieved by the application of Lyapunov-Floquet transformation. Then a completely time-invariant auxiliary system is constructed and order reduction algorithms are applied to this system to obtain a reduced-order system. The control laws are calculated for the reduced-order system by minimizing the least square error between the auxiliary and the transformed system. These control laws are then transformed to obtain the desired control action in the original domain. The schemes formulated arc illustrated by designing full-state feedback and output feedback controllers for a five-mass inverted pendulum exhibiting parametric instability

We address the problem of designing controllers that guarantee asymptotic stability of a class of linear as well as nonlinear dynamical systems with time-periodic coefficients. Using a repeated procedure consisting of the Lyapunov-Floquet transformation, the backstepping technique, and Floquet theory, the asymptotic stability of the closed-loop linearized system is guaranteed. Further, a Lyapunov matrix for the closed-loop asymptotically stable linearized system is constructed. This Lyapunov function is then used to design a combination of linear and nonlinear controllers in order to guarantee the asymptotic stability of the nonlinear system. The methodology is illustrated by designing linear and nonlinear control laws for a system consisting of two statically coupled pendula, each subjected to a time-periodic force acting in the axial direction.

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