Adaptive output feedback control of general MIMO systems using multirate sampling

In adaptive output feedback control based on almost strictly positive real conditions, a technical difficulty arises when the multi-input multi-output (MIMO) system under consideration is non-square, and in particular, has less inputs than outputs. To overcome this, we propose an idea of multirate sampled-data control. That is, a lifted discrete-time system, which has the same number of inputs and outputs and does not give rise to the causality constraint, is made by carefully choosing faster input sampling rates. The output feedback based adaptive control strategy can then be applied to the lifted system under certain conditions. The results reported here are validated on numerical simulations through a cart-crane model.