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LMI conditions for robust adaptive control of LTI systems

Alexander Fradkov, Dimitri Peaucelle
Passification-based direct adaptive control is considered for polytopic uncertain linear time-invariant systems. Linear Matrix Inequality based results are provided to guarantee that the adaptive algorithm passifies the system whatever the uncertain parameters in some given set. The contributions are based on the introduction of a parallel feed-forward shunt that liberates from the strong equality constraint $PB=C^TG^T$ often used for strict passification. The shunt, combined with the introduction of slack variables, allows to conclude with easy to test conditions without restrictions on which data is uncertain in the process model. A simple academic example illustrates the results.
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