A Unified LMI Conditions for Parameter Estimation Impedance Control Strategy with Time Delay of Mechanical Systems

In mechanical system control, time delays and inaccurate parameter estimation stand as critical factors that impair control performance. This paper extends traditional impedance control frameworks by incorporating time-varying delays and developing a systematic identification methodology using the dynamic regressor extension and mixing technique for parameter estimation. By applying the Schur complement lemma, the complex Lyapunov derivative is transformed into a tractable linear matrix inequality formulation. Systematic manipulation of matrix inequalities ensures its negative definiteness, providing a robust stability guarantee. Simulation results validate the effectiveness of the proposed algorithm.