Journal
ISA TRANSACTIONS
Volume 51, Issue 1, Pages 65-73Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.isatra.2011.07.010
Keywords
Fractional order switched system; Linear matrix inequality (LMI); Variable structure control
Ask authors/readers for more resources
This paper presents the stabilization problem of a linear time invariant fractional order (LTI-FO I switched system with order 1 < q < 2 by a single Lyapunov function whose derivative is negative and bounded by a quadratic function within the activation regions of each subsystem. The switching law is extracted based on the variable structure control with a sliding sector. First, a sufficient condition for the stability of an LTI-FO switched system with order 1 < q < 2 based on the convex analysis and linear matrix inequality (LMI) is presented and proved. Then a single Lyapunov function, whose derivative is negative, is constructed based on the extremum seeking method. A sliding sector is designed for each subsystem of the LTI-FO switched system so that each state in the state space is inside at least one sliding sector with its corresponding subsystem, where the Lyapunov function found by the extremum seeking control is decreasing. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the Lyapunov function in the state space. Simulation results are given to show the effectiveness of the proposed VS controller. (C) 2011 ISA. Published by Elsevier Ltd. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available