Adaptive control of linear time-varying systems

Single-input single-output uncertain linear time-varying systems are considered, which are affected by unknown bounded additive disturbances; the uncertain time-varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds. The output, which is the only measured variable, is required to track a given smooth bounded reference trajectory. The undisturbed system is assumed to be minimum-phase and to have known and constant relative degree, known sign of the ‘high frequency gain’, known upper bound on the system order. An adaptive output feedback control algorithm is designed which assures: (i) boundedness of all closed-loop signals; (ii) arbitrarily improved transient performance of the tracking error; (iii) asymptotically vanishing tracking error when parameter time derivatives are L₁ signals and disturbances are L₂ signals.