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A Gramian-based controller for linear periodic systems

Abstract:

Many important real-world processes are best modelled by linear time-periodic systems. This paper proposes a new design method for the control of these systems. The method is based on the use of the reachability Gramian and a specific form for the feedback gain matrix to build a novel control law for the dosed-loop system. The new controller is presented as full-state and allows the control engineer to assign all the invariants of the system; i.e., the full monodromy matrix. Calculation of the feedback matrix requires solving a matrix integral equation for the periodic Floquet factor of the new state-transition matrix of the dosed-loop system. The effectiveness of the method is illustrated on a simple example.

Authors: Pierre Montagnier, Raymond Spiteri

Download: TAC2002