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Linear periodic systems: Eigenvalue assignment using discrete periodic feedback. (English) Zbl 0657.93024
This note discusses the eigenvalue assignment problem of a T-periodic linear system using discrete periodic state feedback gains. For controllable systems, an explicit formula for the feedback law is given that can be used for the arbitrary assignment of the eigenvalues of $$\Phi_{cl}(T,0)$$, the closed-loop state transition matrix from 0 to T. Also, for the special case of periodic systems controllable over one period, this control law can be used to obtain any desired $$\Phi_{cl}(T,0)$$.

##### MSC:
 93B55 Pole and zero placement problems 93C05 Linear systems in control theory 34C25 Periodic solutions to ordinary differential equations 49M99 Numerical methods in optimal control
time-dependent
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