Linear Periodically Time-varying Research Articles

PIPELINED-BLOCK MODELS OF LINEAR DISCRETE-TIME SYSTEMS

For pipelining and block processing in linear time-varying (LTV), linear periodically time-varying (LPTV), and linear time-invariant (LT!) discrete-time systems, we suggest to use the general solution of state space equations. First, we develop three pipelined-block models for LTY, LPTY, and LT! discrete-time systems, and two pipelined-block structures. Afterwards, we analyse complete state controllability, com­ plete output controllability, and complete observability of LTV and LT! pipelined-block discrete-time systems.

Minimization of the Peak-to-Peak Gain in Periodic Systems Under Full State Feedback

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).

Inversion of linear periodically time-varying digital filters

This paper discusses the inversion of linear periodically time-varying (LPTV) digital filters using the idea of converting the LPTV filter to the block time-invariant filter. Explicit expressions are given to determine the inversion of LPTV filters. Controllability and observability of the inversion of LPTV filters are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Invertibility of linear periodically time-varying filters

The invertibility of linear periodically time-varying (LPTV) filters is addressed. A necessary and sufficient condition under which a LPTV filter can be inverted is shown using a LPTV postfilter. Such techniques find application, for example, in aliasing cancellation in multirate systems. >

Minimization of the Peak-to-Peak Gain in Periodic Systems Under Full State Feedback1

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).