Adaptive Delayed Implementation of Derivative-Dependent Control for Nonlinear Systems With Biased Measurements

We study derivative-dependent control of nonlinear systems with external disturbances, where the output with a time-varying and unknown bias that may be induced by a sensor error is available for the measurements. The derivatives are approximated via finite-difference resulting in a delay-dependent feedback that is dependent on the measurement and the estimation of the unknown bias as well as their past. To address the estimation of the unknown bias, we design a high-order adaptive law through the σ-modification method. We next apply the Lyapunov-Krasovskii approach to establish sufficient conditions for input-to-state stability (ISS), which are formulated in terms of linear matrix inequalities (LMIs). Then criterion for designing the gains of the delay-dependent feedback and adaptive law is presented leading to a minimization problem with solvable LMIs rather than the linear constraints. Moreover, we suggest its sampled-data implementation by using the consecutively sampled output and bias’s estimation, where the design criterion for finding the gains of the sampled-data feedback and adaptive law is presented. The proposed method is validated by two simulation examples including a practical inverted pendulum on a cart.