Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach

Md Saat, Mohd Shakir (2013) Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach. Circuits, Systems, and Signal Processing, Volume 33 (2). pp. 331-346. ISSN 1531-5878

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Abstract

This paper investigates the problem of designing a nonlinear H ∞ state feedback controller for polynomial discrete-time systems with norm-bounded uncertainties. In general, the problem of designing a controller for polynomial discrete-time systems is difficult, because it is a nonconvex problem. More precisely, in general, its Lyapunov function and control input are not jointly convex. Hence, it cannot be solved by semidefinite programming. In this paper, a novel approach is proposed, where an integrator is incorporated into the controller structure. In doing so, a convex formulation of the controller design problem can be rendered in a less conservative way than the available approaches. Furthermore, we establish the interconnection between robust H ∞ control of polynomial discrete-time systems with norm-bounded uncertainties and H ∞ control of scaled polynomial discrete-time systems. This establishment allows us to convert the robust H ∞ control problems to H ∞ control problems. Then, based on the sum of squares (SOS) approach, sufficient conditions for the existence of a nonlinear H ∞ state feedback controller are given in terms of solvability of polynomial matrix inequalities (PMIs), which can be solved by the recently developed SOS solvers. A tunnel diode circuit is used to demonstrate the validity of this integrator approach

Item Type:	Article
Subjects:	T Technology > TK Electrical engineering. Electronics Nuclear engineering
Divisions:	Faculty of Electronics and Computer Engineering > Department of Industrial Electronics
Depositing User:	DR. Mohd Shakir Md Saat
Date Deposited:	13 Feb 2014 00:41
Last Modified:	28 May 2015 04:15
URI:	http://eprints.utem.edu.my/id/eprint/11076
Statistic Details:	View Download Statistic

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