A Backstepping Based Dynamic Surface Control Method for a Class of Non-lower Triangular Nonlinear Systems

An approach of tracking control design was presented for a class of non-lower triangular nonlinear systems by combining techniques of backstepping and dynamic surface control. At each step of design, a backstepping based virtual control law or actual control law was established to stabilize the corresponding subsystem. To deal with circular structure problem of control, a first-order low-pass filter was employed to process virtual control signal at each intermediate step of recursive design. Stability results of the closed-loop system showed that all signals are semi-globally uniformly ultimately bounded. Further more, the steady-state tracking error can be guaranteed to converge to an arbitrarily small neighborhood of zero by choosing parameters appropriately. The efficacy of the design was demonstrated via a simulation example.