Title of article :
Sufficient condition for stabilization of linear time invariant fractional order switched systems and variable structure control stabilizers
Author/Authors :
Balochian، Saeed نويسنده Department of Electrical Engineering, Gonabad Branch, Islamic Azad University, Gonabad, Iran , , Saeed and Sedigh، نويسنده , , Ali Khaki، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2012
Pages :
9
From page :
65
To page :
73
Abstract :
This paper presents the stabilization problem of a linear time invariant fractional order (LTI-FO) 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.
Keywords :
Variable structure control , Fractional order switched system , Linear matrix inequality (LMI)
Journal title :
ISA TRANSACTIONS
Serial Year :
2012
Journal title :
ISA TRANSACTIONS
Record number :
2383140
Link To Document :
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