Stability Analysis and Adaptive Controller Design for a Class of Nonsmooth Systems

摘要

In this paper a solid stability analysis and control designs for an affine system with discontinuity are proposed. Since the nonsmooth system considered is not necessarily stabilized by any Lipschitz continuous controller, we introduce discontinuous controllers. If the upper and lower bounds of discontinuous uncertainty are available, a modifying L_gV structure-based switching controller can be applied, and the stability and the uniqueness of the Filippov solution are assured. In a case that the upper and lower bounds of the uncertainty are not available, we show an adaptive control approach to assure the strong stability and attractiveness of the state of the controlled system whereas a classical adaptive control methodology can not be applied due to the discontinuity. Throughout the paper, we consistently employ the concept of the Filippov solution.