Robustification of time varying linear quadratic optimal control based on output integral sliding modes

A hierarchical observer for an uncertain linear time-varying system is designed generalising the output integral sliding-mode approach. The observer is based on a step by step reconstruction of the output and its derivatives, to reconstruct the state theoretically exactly right after the initial time, eliminating completely the effects of the uncertainties/perturbations. The observed state is used in linear quadratic control with an output integral sliding-mode technique, allowing the uncertain system to behave as a nominal (uncertainties/perturbations free) one. The proposed approach is tested by computer simulations.