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To study the problem of improving transient tracking performance for nonlinear systems, this paper proposes an additive-state-decomposition-based control method for a class of nonlinear nonminimum phase (NMP) systems. This method ‘additively’ decomposes the original problem into two more tractable problems, namely a tracking problem for a linear time-invariant NMP ‘primary’ system and a state stabilisation problem for a certain nonlinear ‘secondary’ system. Then, controller for each system is designed respectively by employing existing methods, i.e. the linear quadratic regulator (LQR) method for the primary system and the backstepping method for the secondary system. Next, these two controllers are combined together to achieve the original tracking goal. Furthermore, the adjustment of weighting matrix Q in the LQR regulates the transient response of the closed-loop nonlinear system. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed method.

Besides parametric uncertainties and disturbances, unmodelled dynamics and time delay at the input are often present in practical systems, and cannot always be ignored. This paper aims to solve the problem of output feedback tracking control for a class of non-linear uncertain systems subject to unmodelled high-frequency gains and time delay in the input. By additive state decomposition, the uncertain system is transformed to an uncertainty-free system, in which the uncertainties, disturbances and effects of unmodelled dynamics along with time delay are lumped into a new disturbance at the output. Subsequently, additive state decomposition is used to decompose the transformed system to simplify the tracking controller design. The proposed control scheme is applied to three benchmark examples to demonstrate its effectiveness.

A new stability theorem of the direct Lyapunov's method is proposed for neutral-type systems. The main contribution of the proposed theorem is to remove the condition that the 𝒟 operator is stable. In order to demonstrate the effectiveness, the proposed theorem is used to determine the stability of a neutral-type system in a critical case, i.e. the dominant eigenvalues of the principal neutral term (matrix D in Introduction) lie on the unit circle. This is difficult or infeasible in previous studies.