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

Highlights：

• Because of the particularity of Riemann-Liouville fractional operator, a control scheme involving discontinuous switching factor and fractional-order derivative term is proposed, where fractional-order derivative term is designed to address the initial values that appear during the calculation.

• A state-dependent switching signal is constructed together with switched control scheme to deal with the unknown nonlinearity, where the classification and treatment of different time intervals with respect to fractional order switching and system mode switching can be perfectly avoided while constructing multiple Lyapunov functionals.

摘要

•The stabilization of non-smooth fractional variable-order switched systems with all subsystems unstable in Riemann-Liouville sense in the presence of unknown nonlinearity is firstly investigated, where the variable-order fractional derivative and system modes are both switched, but not limited to synchronous switching.•Because of the particularity of Riemann-Liouville fractional operator, a control scheme involving discontinuous switching factor and fractional-order derivative term is proposed, where fractional-order derivative term is designed to address the initial values that appear during the calculation.•A state-dependent switching signal is constructed together with switched control scheme to deal with the unknown nonlinearity, where the classification and treatment of different time intervals with respect to fractional order switching and system mode switching can be perfectly avoided while constructing multiple Lyapunov functionals.