Non-smooth finite-time adaptive stabilisation of cascade switched systems with asymmetric output constraints

In this article, the problem of non-smooth finite-time (FT) adaptive state feedback stabilisation is investigated for asymmetric output-constrained cascade switched nonlinear systems (AOCCSNSs) with mixed powers, parametric uncertainties and zero dynamics. To better address the uncertain parameters and the asymmetric output constraints, a new type of common Lyapunov function (CLF) including a quadratic squared term of the estimated error and a tangent-type barrier Lyapunov function (Tt-BLF) is constructed. Then, with some mild assumptions, such as input-to-state stability (ISS) property of zero dynamics, upper boundedness of subsystems' nonlinear terms and some well-known small signal conditions, state feedback controllers (SFCs) constructed by adding a power integrator (AAPI) technique and the update law to estimate the unknown parameter are proposed to guarantee resultant closed-loop switched systems FT stable. The proposed method for switched systems is presented in a unified manner, capable of addressing FT stabilisation by effectively handling situations with or without output constraints. This is achieved through the construction of Tt-BLF, which degenerates into a quadratic form when the output constraint disappears or approaches infinity. At last, the method is verified by a switched RLC circuit system (RLC-CS) and a numerical simulation.