New approach to robust stability analysis of sampled-data control systems

The lifting technique is now the most popular tool for dealing with sampled-data control systems. However, for the robust stability problem the system norm is not preserved by the lifting as expected. And the result is generally conservative under the small gain condition. The reason for the norm difference by the lifting is that the state transition operator in the lifted system is zero in this case. A new approach to the robust stability analysis is proposed. It is to use an equivalent discrete-time uncertainty to replace the continuous-time uncertainty. Then the general discretized method can be used for the robust stability problem, and it is not conservative. Examples are given in the paper.