Input-to-State stability and inverse optimality of linear Time-Varying-Delay predictor feedbacksInput-to-State stability and inverse optimality of linear Time-Varying-Delay predictor feedbacks Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2018-05-082017enFor linear systems with time-varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal, with respect to a meaningful differential game problem, and establish its robustness to constant multiplicative perturbations appearing at the system input. Both of these properties of the basic predictor feedback controller have not been established so far, even for the constant-delay case. We then show that the basic predictor feedback controller, when applied through a low-pass filter, is again inverse optimal and study its input-to-state stability as well as its robustness, to the low-pass filter time constant, properties. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation, which allows us to construct appropriate Lyapunov functionals. A numerical example is also providedhttp://creativecommons.org/licenses/by/4.0/IEEE Transactions on Automatic Control631233-240 Cai Xiushan Bekiaris-Liberis Nikolaos Μπεκιαρης-Λυμπερης Νικολαος Krstić, Miroslav Institute of Electrical and Electronics Engineers Adaptive control Backstepping Delay systems Delays Disturbance attenuation Input-to-state stabilization Inverse optimality Linear predictor feedback Linear systems Numerical stability Robustness Stability criteria