| The fractional-order/variable-order fractional switched system has the excellent characteristics of fractional-order/variable-order fractional calculus and the powerful application background of switched system.Considering that the system in normal operation is inevitably restricted by the actual environment such as working conditions,there may be equipment failures and other problems,which can easily destroy the stability of the subsystem,thereby affecting the performance of the entire switched system.Hence,it is challenging to take the external factors into the fractional-order/variableorder switched system with partial or all unstable subsystems.In this thesis,the stability of fractional-order/variable-order fractional switched system with external disturbances and unknown nonlinearity is investigated.The specific contents are as follows:Firstly,the asymptotic stabilization and finite-time stabilization of incommensurate fractional-order switched system with unknown nonlinearity and external disturbances are discussed.The unknown function is approximated by neural network,and two kinds of neural network based adaptive controllers are designed to realize the asymptotic stability and finite time stability.As for the latter,the convergence time for the finite time stability of the system is estimated,and the relationship among the convergence time,system initial value and switching signal is established.Secondly,we study the global asymptotic stabilization of general fractional-order nonlinear switched system,where the derivatives of constructed multiple Lyapunov functions are allowed to be indefinite.Under the relaxed restriction that the derivatives of the multiple Lyapunov functions are required to be negative,sufficient criterion for the stability of switched system is established by designing the periodic switching law and using fractional calculus theory.In addition,an algorithm implementation of the periodic switching signal is given along with some in-depth discussions.Thirdly,on the basis of the above two chapters,the constant-order fractional calculus is extended to the variable-order fractional calculus,and the global asymptotic stabilization and finite-time stabilization of the variable-order fractional system with partial prior bounded disturbances are investigated.Via the induction method and Arzel`aAscoli theorem,the existence and uniqueness of the solution of the closed-loop system is verified.Combining variable-order fractional operator with discontinuous adaptive control method,sufficient criteria for the stability of the system are established by using Lyapunov stability theory and non-smooth analysis.Furthermore,the upper bound of convergence time for the finite-time stabilization of the system is evaluated,which is related to the system initial value and disturbance parameters.Then,the switching of variable-order fractional derivative and system modes are considered simultaneously.For Riemann-Liouville fractional-order system,the global asymptotic stabilization issue of the discontinuous variable-order Riemann-Liouville fractional-order switched system with unknown nonlinearity is discussed.Considering that all subsystems are unstable and unknown nonlinear function satisfies certain condition,we co-design a state-dependent switching signal and a discontinuous controller containing the switching term and the Riemann-Liouville fractional derivative term.Sufficient stability criteria are derived by using Lyapunov stability theory and differential inclusion theory.Finally,a mixed fractional-order switched system consisting of fractional-order and integer-order subsystems is modeled,and the stabilization issue of the discontinuous mixed fractional-order switched system with unstable modes is investigated.Slow and fast switching strategies are respectively proposed for stable and unstable subsystems.Under the designed switching controllers,sufficient stability conditions are given by constructing multiple Lyapunov functions and using differential inclusion theory,non-smooth analysis,minimum dwell time and mode-dependent average dwell time method. |
