| As an extension and generalization of integer-order calculus,fractional-order calculus has the superiority of more accurate in describing model,easier in improving control performance and higher freedom in designing controller.With the development of engineering technology,the practical system becomes more and more complex and the requirements on control performance are improved,the controller design of fractional-order systems rapidly becomes a current hot spot.At the same time,the actual dynamics models are nonlinear.Usually,only the system outputs are measurable and the state variables are not easily measured.Therefore,this paper systematically investigates the design of dynamic output feedback controller and stability analysis for fractional-order nonlinear systems with unmeasured state variables.Firstly,the tracking control problem of the system output is investigated for a class of fractional-order nonlinear time-delay systems with quantized inputs in a lower triangular structure.The novel fractional-order filters are designed to reconstruct the unmeasurable state variables of the system.The virtual controller for each step is constructed based on backstepping method so that the control input of the system can be obtained.The fractional-order model is transformed by introducing the frequency distribution model to calculate the first-order derivative of the Lyapunov function,which avoids the problem that it is difficult to find the fractional-order derivative of the Lyapunov-Krasovskii generalized function.The fractional-order Lyapunov method is used to prove the bounded stability of the closed-loop system.Secondly,the tracking control problem of the system outputs is studied for a class of interconnected fractional-order nonlinear systems considering unmodeled dynamics.By designing novel reduced-order high-gain fractional-order filters,the unmeasurable state of the system is reconstructed and the structure of filters is simplified.Based on the backstepping method and adaptive control technique,the dynamic output feedback controller for the interconnected fractional-order system is designed.By combining with the dynamic surface control method,the computational explosion problem that occurs during the traditional backstepping iterative design is avoided.Based on the given assumptions for the unmodeled subsystem,the semi-global bounded stability of the closed-loop system is proved using the fractional-order Lyapunov method.Then,the H_∞output feedback control problem is investigated for a class of uncertain fractional-order T-S fuzzy systems with time-varying delay.By designing a reduced-order fuzzy observer,the dynamic output feedback controller structure is simplified and the unmeasured state of the system is reconstructed.Utilizing matrix analysis method,the number of variables to be decided is reduced by introducing a new matrix to parameterize the gain matrices of observer.Combining with the fractional-order Lyapunov theory,the delay-independent fuzzy controller design strategy is proposed.The linear matrix inequality technique is used to give a solution method for the parameters of the observer and controller matrices,which ensures that the closed-loop system is stable with given H_∞performance index.Furthermore,the output feedback controller design strategy and delay-independent stability analysis are studied for fractional-order nonlinear time-delay systems subject to actuator saturation.A dynamic output feedback controller with higher design freedom and lower implementation cost is given.The stability analysis of the closed-loop system is carried out by the fractional-order Lyapunov method.The sufficient conditions in the form of linear matrix inequalities for the asymptotic stability of the closed-loop system are proposed.Further,the optimization conditions for estimating domain of attraction are given,which can reduce conservatism.Finally,dynamic output feedback controller and stability criterion of delay-dependent and order-dependent are given for fractional-order nonlinear time-delay system with actuator saturation.Using the fractional-order Razumiklin theory,the sufficient conditions for asymptotic stability of closed-loop systems with low conservatism and the solution method of enlarging the estimation for domain of attraction are derived.Two new auxiliary matrix forms and a novel convexification treatment of non-convex stability conditions are proposed.The design method of the controller gain matrices is given. |
