Stabilization of Fractional-Order Systems Subject to Saturation Element Using Fractional Dynamic Output Feedback Sliding Mode Control

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Esmat Sadat Alaviyan Shahri ◽  
Alireza Alfi ◽  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Linear Component ◽  
Dynamic Output Feedback ◽  
Closed Loop System ◽  
Fractional Systems ◽  
Dynamic Output ◽  
System States

This paper addresses the design of a robust fractional-order dynamic output feedback sliding mode controller (FDOF-SMC) for a general class of uncertain fractional systems subject to saturation element. The control law is composed of two components, one linear and one nonlinear. The linear component corresponds to the fractional-order dynamics of the FDOF-SMC, while the nonlinear component is associated with the switching control algorithm. The closed-loop system exhibits asymptotical stability and the system states approach the sliding surface in a finite time. In order to design the controller, a linear matrix inequality (LMI)-based procedure is also derived. Simulation results demonstrate the feasibility of the FDOF-SMC strategy.

Tracking of Periodic Trajectories for Switched Systems Under Time-Varying Asynchronous Switching

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Guoqi Ma ◽  
Xinghua Liu ◽  
Prabhakar R. Pagilla ◽  
Shuzhi Sam Ge
Keyword(s):  
Output Feedback ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Decomposition Approach ◽  
Dynamic Output ◽  
2D Model ◽  
Repetitive Controller

In this technical brief, we provide an asynchronous modified repetitive controller design to address the periodic trajectory tracking problem for switched systems with time-varying switching delays between plant modes and controllers. In the feedback channel, a dynamic output feedback mechanism is adopted. By utilizing the lifting technique, the dynamic output feedback-based switched repetitive control system is transformed into a continuous-discrete two-dimensional (2D) model to differentiate the control and learning actions involved in the repetitive controller. For the transformed 2D model, by constructing a piecewise Lyapunov functional and utilizing a matrix decomposition approach, sufficient conditions in terms of linear matrix inequalities (LMIs) and the average dwell time are developed to guarantee closed-loop exponential stability. The performance of the proposed approach is illustrated via a switched RLC series circuit example and numerical simulations are provided.

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