The paper considers the minimization of the $l∞$-induced norm of the closed loop in linear periodically time varying (LPTV) systems when state information is available for feedback. A state-space approach is taken and concepts of viability theory and controlled invariance are utilized. It is shown that a memoryless periodically varying nonlinear controller can be constructed to achieve near-optimal performance. The construction involves the solution of several finite linear programs and generalizes to the periodic case earlier work on linear time-invariant systems (LTI).

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