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This study presents a fault-tolerant continuous super-twisting control algorithm for dynamical systems, subject to Lipshitzian and non-Lipshitzian bounded disturbances. The conditions of finite-time convergence of the entire system state to the origin are obtained. An experimental verification of the designed fault-tolerant algorithm is conducted for a DTS200 three-tank system through varying fault sources, disturbances, input conditions and inter-tank connections. IntroductionIt is well-known that the classical discontinuous sliding mode control provides finite-time convergence for a scalar system state [1]. A finite-time stabilising control for a system of dimension two is realised using the twisting algorithm [2], where the secondorder sliding mode control is also discontinuous. Both algorithms are robust with respect to bounded disturbances. On the other hand, using a continuous second-order sliding mode super-twisting algorithm [3], a scalar system state can be stabilised along with its first derivative. The super-twisting algorithm is robust with respect to unbounded disturbances satisfying a Lipschitz condition. A recent paper [4] has presented a modified super-twisting algorithm for systems of dimension more than one, which is, however, robust only against disturbances satisfying a Lipschitz condition. This paper presents a fault-tolerant homogeneous continuous super-twisting control algorithm for dynamical systems, subject to not only Lipshitzian and but non-Lipshitzian bounded disturbances as well, thus making a substantial advance with respect to existing results. The conditions of finite-time convergence of the entire system state to the origin are obtained. First, the case of dimension two is addressed. Similar results are then obtained for systems of dimension more than two. The paper concludes with an experimental verification of the designed fault-tolerant algorithm, which is conducted for a DTS200 three-tank system through varying fault sources, disturbances, input conditions and inter-tank connections. This three-tank system is a widely recognised testbed for applying performance tests and validating new control strategies [5]. Making use of its built-in fault scenarios (sensor fault, actuator fault and process fault), the three-tank system has been actively employed for research in the areas of fault detection and diagnosis [6-10] and fault-tolerant control design [7,[11][12][13][14].The paper is organised as follows. The problem statement is given in Section 2. A fault-tolerant continuous super-twisting control algorithm for dynamical systems is designed in Section 3. An experimental verification of the designed fault-tolerant algorithm is conducted for a DTS200 three-tank system in Section 5. The proofs of all theorems are given in the Appendix. 2Control problem statement for faulted systems Consider a dynamic system of dimension two in the presence of faultẋ∈ R 2 is the system state and u(t) ∈ R is the control input. The function f (x 1 (t), x 2 (t), t) satisfies the Lipschitz condition with...

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