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Singular systems with matched Lipschitz perturbations and uncertainties are considered in this paper. Since continuous solutions of an impulse-free singular system require continuous input signals, a two-step continuous sliding-mode control strategy to compensate matched Lipschitz perturbations and uncertainties in singular systems is proposed. Our suggested methodology is tested in a singular representation of a DC motor pendulum of relative degree two. The performance of the proposed strategy is assessed by comparing the accuracy, in both cases, with and without considering small noise in the output, obtained through other continuous sliding-mode control, and reconstruction/compensation of perturbations and uncertainties techniques.Recently, CSM controllers for sliding outputs of relative degree r have been developed. Such controllers provide:1. finite-time theoretically exact compensation of Lipschitz P/U; 2. sliding accuracy of order (r+1) with respect to the output ((r+1)th order of precision) in the face of time discretizations of the control input and actuator time constant; 3. robust convergence of the output and its first r time derivatives to the origin in finite time ((r + 1)-sliding motion) while assuming only the information of the output and its first (r − 1) time derivatives.Examples of CSM controllers for systems of relative degree two are: continuous twisting (CT) algorithm, 17 continuous terminal SM, 18 and discontinuous integral controller. 19 For an arbitrary relative degree, continuous algorithms have also been derived (eg, see other works [19][20][21][22] ).

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In this article, a second‐order system, which is affected by disturbances and uncertainties, with a saturating actuator is considered. A novel robust feedback control law is designed based on the sliding mode technique. The twisting and the continuous twisting algorithms are incorporated into the design, which is based on level curves of a Lyapunov function. The performance of the standard continuous twisting algorithm is greatly improved in the case that the initial condition of the system is far away from the origin. A parameter setting for the controller is given by establishing global finite‐time stability properties of the closed‐loop system origin. Feasibility and effectiveness of the proposed approach are indicated in a real‐world application as well as numerical simulation.