Lyapunov-based backstepping control of a class of linear systems without overparametrization, tuning functions or nonlinear damping

The adaptive backstepping approach has been an effective tool in control of uncertain linear systems. However, its traditional recursive non-linear design is complicated, especially for a plant whose relative degree is high. This paper proposes a Lyapunov-based linear backstepping control scheme for a kind of uncertain linear systems whose relative degree is identical with its system dimension. The global stability and asymptotic convergence of the closed-loop system are guaranteed.