LMI conditions for robust adaptive control of MIMO LTI systems1

Passification-based direct adaptive control is considered for polytopic uncertain linear time-invariant multi-input multi-output 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 = CT GT often used for strict passification. The shunt, combined with the introduction of slack variables, allows to produce results without assumptions on which data is uncertain in the process model. Formulas proving robust passification are formulated as Linear Matrix Inequality and can therefore be efficiently tested. A simple academic example illustrates the results.