Global Finite-Time Nonlinear Observers for a Class of Nonlinear Systems Subjected to Mismatched Uncertainties

In this paper, two different types of global finite- time nonlinear observers are designed for a class of nonlinear systems in the presence of matched and mismatched uncertainties. The considered class of nonlinear systems, which is a chain of interconnected second order subsystems, covers many practical plants such as robot manipulators and unmanned aerial vehicles. Therefore, the proposed observers are applicable to a wide group of real-world nonlinear systems. Based on finite-time stability's lemmas, it is mathematically proven that estimated states precisely reach state variables within finite times. More, it is demonstrated these mentioned convergence times are finite and their upper bounds depend on initial conditions and arbitrary parameters of proposed nonlinear observers. Finally, two types of the finite-time observers are simulated onto a 2-DOF robot manipulator to estimate angular velocities of robot's joints.