| Many practical problems in engineering can be modelled as linear dynamical systems with periodically varying coefficients. This thesis proposes a new design method for the control of these linear time-periodic systems.; First, Floquet-Lyapunov theory is used to derive the Floquet factors of the state-transition matrix of a given system. We introduce a novel approach to obtain every real representation. It is demonstrated that the periodicity of the periodic factor can be determined a priori using a constant matrix, which we call the Yakubovich matrix, based upon the signs of the eigenvalues of the monodromy matrix. We then introduce a novel method for the numerical computation of the Floquet factors, relying upon a boundary-value problem formulation and the Yakubovich matrix.; In the second part, we use the invertibility of the controllability Gramian and a specific form for the feedback gain matrix to build a novel control law for the closed-loop system. The new controller can be full-state or observer-based and allows the control engineer to assign all the invariants of the system, i.e. the full monodromy matrix. Deriving the feedback matrix requires first solving a matrix integral equation for the periodic Floquet factor of the new state-transition matrix of the closed-loop system. This is achieved via a spectral method, which can then be further refined by a boundary-value problem formulation. Computational efficiency of the scheme may be further improved by performing the controller synthesis on the transformed system obtained from the reducibility theorem.; Finally, the effectiveness of the method is illustrated with an application to a quick-return mechanism using a software toolbox developed for MATLAB™. |
