Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid  

作　　者：Mohammad Hejri 

机构地区：[1]Department of Electrical Engineering,Sahand University of Technology,Sahand New Town,Tabriz 51335-1996,Iran

出　　处：《IEEE/CAA Journal of Automatica Sinica》2021年第11期1837-1851,共15页自动化学报（英文版）

摘　　要：This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via statedependent switching rules.Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid.These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type.In some cases,the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function.In this paper,we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently.The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size.Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size,i.e.,a purely numerical method and a numerical-analytical one.In the former,both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities.The latter is established on a principle that the attractiveness of a set implies its invariance.Thus,the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension.Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.

关 键 词：Decentralized quadratic Lyapunov function decentralized ellipsoid discrete-time switched affine systems practical stabilization switching power converters 

分 类 号：O19[理学—数学]