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# Simultaneous Stabilization of Linear Time Varying Systems by Linear Time Varying Compensation

## Abstract

The problem of stabilization of a linear time-invariant plant by a linear time-invariant output feedback compensator has been one of the most important problems in system theory. However, since many of the systems considered in practice are time-varying, it is important to generalize results well known in time-invariant systems theory (see [4], [5], [6], [7]) to the time-varying case. It is for this reason we consider the following problem:

*Problem* 1.1: (Stabilizability Problem) Given a discrete-time multi-input multi-output linear time-varying dynamical system, does there exist a linear time-varying dynamic compensator which robustly stabilizes the system in the closed-loop?

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