Combining the MIT and Lyapunov stability adaptive methods for second order systems

In this paper, two adaptive control methods introduced in literature (e.g. the gradient and Lyapunov stability methods) are applied on several theoretical examples considering the second order plant for different time varying parameters. Further on, two new adaptive control laws are proposed. The first one is based on MIT rule and Lyapunov stability combination to allow usage of the same value for all adaptation gains. The second one, based on the first one, is developed for perturbation rejection by adding an artificial perturbation at the plant's input. Using Matlab / Simulink, the preferred approach for each use case is showcased.