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On the Stabilization of Linear Time Invariant Fractional Order Commensurate Switched Systems
Author(s) -
Balochian Saeed
Publication year - 2015
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.858
Subject(s) - control theory (sociology) , linear matrix inequality , lti system theory , mathematics , lyapunov function , linear system , controller (irrigation) , convex optimization , stability (learning theory) , state space , regular polygon , computer science , mathematical optimization , control (management) , nonlinear system , mathematical analysis , agronomy , physics , geometry , quantum mechanics , artificial intelligence , biology , statistics , machine learning
Abstract In this paper, the stabilization problem of a linear time invariant fractional order ( LTI‐FO ) switched system is outlined. First, the sufficient condition for stability of a commensurate LTI‐FO switched system based on the convex analysis and linear matrix inequality ( LMI ) is presented. Then, a single Lyapunov function is constructed based on the optimization method. Then, 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 L yapunov function found by the optimization method is decreasing. Finally, a switching control law is designed to switch the LTI‐FO switched system among subsystems to ensure the decrease of the L yapunov function in the state space. Simulation results are given to show the effectiveness of the proposed variable structure controller.