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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| Vydáno v: | IET control theory & applications Ročník 7; číslo 13; s. 1699 - 1710 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Stevenage
The Institution of Engineering and Technology
01.09.2013
John Wiley & Sons, Inc |
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| ISSN: | 1751-8644, 1751-8652 |
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| Abstract | 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. |
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| AbstractList | 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. 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. [PUBLICATION ABSTRACT] |
| Author | Liang, Jinling Wang, Zidong Liu, Xiaohui |
| Author_xml | – sequence: 1 givenname: Jinling surname: Liang fullname: Liang, Jinling email: jinlliang@seu.edu.cn organization: 1Department of Mathematics, Southeast University, Nanjing 210096, People's Republic of China – sequence: 2 givenname: Zidong surname: Wang fullname: Wang, Zidong organization: 3Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK – sequence: 3 givenname: Xiaohui surname: Liu fullname: Liu, Xiaohui organization: 3Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK |
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| Keywords | 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 |
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| Snippet | This study addresses the robust stabilisation problem for the two-dimensional (2D) discrete non-linear stochastic systems with time-varying delays in states.... This study addresses the robust stabilisation problem for the two‐dimensional (2D) discrete non‐linear stochastic systems with time‐varying delays in states.... |
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| SubjectTerms | 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 |
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| Title | Robust stabilisation for a class of stochastic two-dimensional non-linear systems with time-varying delays |
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