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Nonlinear H ∞ output feedback control with integrator for polynomial discrete‐time systems
Author(s) -
Saat Shakir,
Nguang Sing Kiong
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3130
Subject(s) - integrator , semidefinite programming , control theory (sociology) , lyapunov function , nonlinear system , convex optimization , polynomial , controller (irrigation) , double integrator , solver , mathematics , discrete time and continuous time , nonlinear control , explained sum of squares , optimal control , regular polygon , mathematical optimization , computer science , control (management) , computer network , mathematical analysis , statistics , physics , geometry , bandwidth (computing) , quantum mechanics , artificial intelligence , agronomy , biology
Summary This paper investigates the problem of designing a nonlinear H ∞ output feedback controller for a class of polynomial discrete‐time systems. In general, this problem is hard to be formulated in a convex form because the relation between the control input and the Lyapunov function is always not jointly convex. Therefore, the problem cannot be solved via semidefinite programming (SDP). On the basis of the sum of squares (SOS) approach and incorporation of an integrator into the controller, sufficient conditions for the existence of a nonlinear H ∞ output feedback controller are given in terms of SOS conditions, which can be solved by an SDP solver. In contrast to the existing methods, a less conservative result is obtained. Finally, numerical examples are used to demonstrate the validity of this integrator approach. Copyright © 2013 John Wiley & Sons, Ltd.