Partial stabilization of uncertain nonlinear systems

In this paper, the problem of robust partial stabilization is considered and two approaches for partial stabilization of uncertain nonlinear systems are presented. In these approaches, the nonlinear dynamical system is divided into two subsystems, which are called the first and the second subsystems. This division is done based on the required stability properties of the system’s states. The reduced input vector (the vector that includes components of the input vector appearing in the first subsystem) is designed to asymptotically stabilize the first subsystem. In the first approach, a new partial stabilization technique, based on the first order sliding mode control idea is proposed. In the proposed method, hereafter called the partial sliding mode, a sliding surface is designed such that restricting the motion on this surface guarantees the stability of only the first part of the system’s state. In the second approach, a Lyapunov-based controller is proposed for partial stabilization and then an additional feedback control is designed so that the overall feedback law guarantees a robust manner in the presence of uncertainties. ► We propose two approaches for robust stabilization of uncertain nonlinear systems. ► We consider stability with respect to a part of system’s state. ► We called our first method the “partial sliding mode”. ► Also, a Lyapunov-based controller was proposed for robust partial stabilization.