A New Approach to Robust Stability Analysis of Sampled-data Control Systems

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The lifting technique is now the most popular tool for dealing with sampled-data controlsystems. However, for the robust stability problem the system norm is not preserved by the liftingas expected. And the result is generally conservative under the small gain condition. The reason forthe norm di?erence by the lifting is that the state transition operator in the lifted system is zero inthis case. A new approach to the robust stability analysis is proposed. It is to use an equivalentdiscrete-time uncertainty to replace the continuous-time uncertainty. Then the general discretizedmethod can be used for the robust stability problem, and it is not conservative. Examples are givenin the paper. The lifting technique is now the most popular tool for dealing with sampled-data controlsystems. However, for the robust stability problem the system norm is not preserved by the liftingas expected. And the result is generally conservative under the small gain condition. The reason forthe norm di? erence by the lifting is that the state transition operator in the lifted system is zero inthis 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 discretizedmethod can be used for the robust stability problem, and it is not conservative. Examples are givenin the paper.
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