Robust adaptive L2L2-gain control of polytopic MIMO LTI systems — LMI results

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. Contributions are based on the introduction of a parallel feed-forward shunt that liberates the strong equality constraint PB=CTGT often used for strict passification. The shunt, combined with the introduction of slack variables, allows a conclusion with easy to test conditions without restrictions on which data is uncertain in the process model. The resulting adaptive control is such that control gain is bounded in a chosen set whatever the bounded disturbance. Moreover, it proves to be not worse than computable parameter-dependent static output-feedback controls with respect to L2L2 gain attenuation. A simple academic example illustrates the results.