Stabilization of nonlinear systems with a slowly varying parameter by a control Lyapunov function

Based on a control Lyapunov function (CLF) strategy, a novel approach for designing a controller for a slowly varying nonlinear system is proposed. The approach may be thought of as being in between the time-invariant and time-varying CLF techniques. If the time-invariant technique is used to control a slowly varying system, stability will not be guaranteed. On the other hand, the time-varying CLF technique, due to the control law, has complexity and needs to measure or estimate the derivative of system parameters. The advantage of the proposed method is its independence from the measurement or estimation of the derivatives of the system parameters. It is shown that the proposed control law can even be independent of the parameters of the system. In this paper, the conditions are derived that allow using the simple CLF formula that guarantees the stability of a slowly varying system. The efficiency of the approach is shown through some simulations.