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Summary This paper considers output tracking of nonstep reference signals for multi‐input multi‐output singular systems subject to actuator saturation and external disturbances. Singularity of the system alongside the actuator saturation constraint and external disturbances adds more complexity to stability analysis and controller design than normal systems. Moreover, the problem of output tracking of nonstep reference signals in singular systems via the composite nonlinear feedback (CNF) control law is not studied so far in the literature, and this article will investigate this problem for the first time by proposing the modified CNF control law. For this purpose, first, a singular reference generator system is constructed to produce the desired nonstep reference signal. Then, the dynamical error system is obtained by defining a new state vector as the tracking error and augmenting it to the main system. Different parts of the modified CNF control law are designed afterwards. Due to complexities caused by the singularity of the system and the saturation constraint, detailed mathematical calculations are done. In this regard, a theorem is given that guarantees the tracking problem for three different cases of the saturation function. Moreover, the given theorem will investigate the uniform ultimate boundedness analysis of the tracking error in the face of external disturbances. Finally, the theoretical results are affirmed by computer simulations through three examples to verify the performance and applicability of the proposed control law.

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A low-conservative composite nonlinear feedback controller is proposed for singular time-delay systems with time-varying delay. The proposed composite nonlinear feedback controller not only improves the transient responses of the closed-loop system but it also has less conservatism than other composite nonlinear feedback controllers. The gain of the linear part of the composite nonlinear feedback controller is obtained by precise mathematical calculation to depend not only on the upper bound of the delay but also on the delay range and rate of its changes. More advantages of the proposed composite nonlinear feedback controller are its accurate operation in the presence of actuator saturation, model uncertainties, and system singularities. The linear and nonlinear parts of the proposed controller are designed by solving a linear matrix inequality problem confirmed through a theorem using Lyapunov stability analysis. The theoretical achievements are endorsed by computer simulation through numerical and practical examples.

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