Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems

Abstract This paper deals with the stabilization problem for non-smooth variable-order Riemann-Liouville fractional switched systems with all modes unstable in the presence of unknown nonlinearity. A controller containing the discontinuous switching item and Riemann-Liouville fractional-order derivative term is firstly designed. By applying fractional order calculation, non-smooth analysis theory and Lyapunov stability theory, some criteria are established under the joint design of controller and state-dependent switching law. An application to variable-order fractional switched permanent magnet synchronous motors is demonstrated and relevant numerical simulations for considered system are given to verify the validity of our designed scheme.