Robust stabilisation for a class of stochastic two-dimensional non-linear systems with time-varying delays

This study addresses the robust stabilisation problem for the two-dimensional (2D) discrete non-linear stochastic systems with time-varying delays in states. Based on the well-known Fornasini–Marchesini local state-space model, a more general 2D discrete non-linear system is considered with both sto...

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Veröffentlicht in:	IET control theory & applications Jg. 7; H. 13; S. 1699 - 1710
Hauptverfasser:	Liang, Jinling, Wang, Zidong, Liu, Xiaohui
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Stevenage The Institution of Engineering and Technology 01.09.2013 John Wiley & Sons, Inc
Schlagworte:	2D discrete nonlinear stochastic systems 2D stochastic nonlinear system Asymptotic properties asymptotic stability control system synthesis convex optimisation algorithms convex programming Delay delay dependent state feedback controller delays Design engineering discrete systems Dynamical systems Fornasini‐Marchesini local state‐space model Inequalities inequality techniques matrix inequalities mean square error methods nonlinear control systems Nonlinear dynamics robust control robust stabilisation problem state feedback stochastic analysis stochastic disturbances stochastic two dimensional nonlinear systems Stochasticity time‐varying delays time‐varying systems Two dimensional Fornasini-Marchesini local state-space model time-varying systems stochastic disturbances discrete systems robust stabilisation problem 2D discrete nonlinear stochastic systems control system synthesis convex programming matrix inequalities asymptotic stability convex optimisation algorithms stochastic two dimensional nonlinear systems inequality techniques delays nonlinear control systems delay dependent state feedback controller robust control 2D stochastic nonlinear system state feedback mean square error methods stochastic analysis time-varying delays
ISSN:	1751-8644, 1751-8652
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Beschreibung
Zusammenfassung:	This study addresses the robust stabilisation problem for the two-dimensional (2D) discrete non-linear stochastic systems with time-varying delays in states. Based on the well-known Fornasini–Marchesini local state-space model, a more general 2D discrete non-linear system is considered with both stochastic disturbances and time-varying delays. Our attention is focused on the design of a delay-dependent state-feedback controller so that the 2D stochastic non-linear system is guaranteed to be globally asymptotically stabilisable in the mean square. By using the stochastic analysis and some inequality techniques, sufficient criteria ensuring the existence of such controllers are derived in terms of matrix inequalities, which can be effectively solved by resorting to some standard convex optimisation algorithms. Furthermore, such stabilisation results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. Finally, a numerical example is provided to demonstrate the applicability of the proposed controller design approach.
Bibliographie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	1751-8644 1751-8652
DOI:	10.1049/iet-cta.2012.0915