Identification and adaptation using Lyaponov´s direct method

This paper attempts a unified presentation of general schemes using Lyapunov´s direct method for (i) the adaptive control and (ii) the identification of multivariable systems. The first part deals with cases where all the state variables of the plant are accessible. In the second part, an adaptive observer is synthesized to identify the plant parameters and to simultaneously estimate the plant state vector, when only the output of the system is accessible.