A Continuous-Discrete ADRC for LTI Systems under Nonuniform Discrete Measurements and External Disturbances

Due to the absence of continuous measurements, designing and analyzing robust controllers or observers for dynamic systems under discrete measurements and external disturbances are crucial topics. The active disturbance rejection controller is an algorithm that estimates and rejects these external disturbances to guarantee robust stability in a closed loop within a dynamical system. However, it must be modified to perform well under discrete measurements. In this work, a continuous-discrete active disturbance rejection controller is designed and analyzed with a time-delayed approach to guarantee asymptotic stability for linear time-invariant systems under nonuniform dis-crete measurements. Hence, the controller based on an observer is coupled with an output predictor, such that linear matrix inequality sufficient solvability conditions are given, allowing to tune the algorithm gains. Lastly, the proposed algorithm is illustrated through an academic example.