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Adaptive robust feedback stabilization for a class of cascaded nonlinear systems with discontinuous connection

Many physical phenomena are usually described as a discontinuous function in differential equation-based model, and the discontinuity causes the difficulty in design a controller with conventional differential equation theory. This paper investigates feedback stabilization problem for a class of cascaded nonlinear systems that the discontinuity appears in the connection path of two subsystems. Filippov-framework will be exploited to analyze the behavior of closed loop systems. First, stabilization with nominal model will be shown and then the design method will be extended to the adaptive controller design for the case with uncertainties in the system model. Numerical examples will be given to demonstrate the effectiveness of the proposed design approach.