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

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.

Quadratic stabilisation of switched affine systems

Minqing Xiao received the Ph.D.degree from Chongqing University,Chongqing,China,in 2008.He is currently a Professor with the College of Mathematics and Informatics,Fujian Normal University,Fuzhou,China.His current research interests include robust control/filter theory,delta operator systems,networked control systems,and switched systems;Guisheng Zhai received his B.S.degree from Fudan University,China,in 1988,and he received his M.E.and Ph.D.degrees,both in system science,from Kobe University,Japan,in 1993 and 1996,respectively.After two years of industrial experience,Dr.Zhai moved to Wakayama University,Japan,in 1998,and then to Osaka Prefecture University,Japan,in 2004.He held visiting professor positions at University of Notre Dame from August 2001 to July 2002,and at Purdue University from March 2016 through February 2017.In April 2010,he joined the faculty board of Shibaura Institute of Technology,Japan,where he currently is a full Professor of Mathematical Sciences.His research interests include large scale and decentralised control systems,robust control,switched systems and switching control,networked control and multi-agent systems,neural networks and signal processing,etc.Dr.Zhai is on the editorial board of several academic journals including IET Control Theory&Applications,International Journal of Applied Mathematics and Computer Science,Journal of Control and Decision,and Frontiers of Mechanical Engineering.He is a Senior Member of IEEE,a member of ISCIE,SICE,JSST and JSME.