Robust ℋ2 sliding mode control for non-linear discrete-time stochastic systems
Robust ℋ2 sliding mode control for non-linear discrete-time stochastic systems
- Author(s): L.F. Ma ; Z.D. Wang ; Z. Guo
- DOI: 10.1049/iet-cta.2008.0524
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- Author(s): L.F. Ma 1 ; Z.D. Wang 2 ; Z. Guo 1
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View affiliations
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Affiliations:
1: School of Automation, Nanjing University of Science and Technology, Nanjing, People's Republic of China
2: Department of Information Systems and Computing, Brunel University, Uxbridge, UK
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Affiliations:
1: School of Automation, Nanjing University of Science and Technology, Nanjing, People's Republic of China
- Source:
Volume 3, Issue 11,
November 2009,
p.
1537 – 1546
DOI: 10.1049/iet-cta.2008.0524 , Print ISSN 1751-8644, Online ISSN 1751-8652
This study is concerned with the sliding mode control (SMC) problem for uncertain non-linear discrete-time stochastic systems with ℋ2 performance constraints. The non-linearities considered are of both the matched and unmatched forms, which can encompass several classes of well-studied non-linearities. A new discrete-time switching function is proposed and then a sufficient condition is derived which ensures both the exponentially mean-square stability and the ℋ2 performance in the sliding surface. Such a condition is expressed as the feasibility of a set of linear matrix inequalities (LMIs) with an equality constraint. An improved discrete-time reaching condition is established to obtain the required SMC controller capable of driving the state trajectories onto the specified switching surface, along which then resulting in a non-increasing zigzag-type sliding motion. A simulation example is given to show the effectiveness of the proposed method.
Inspec keywords: H∞ control; linear matrix inequalities; variable structure systems; asymptotic stability; robust control; nonlinear control systems; discrete time systems; uncertain systems; stochastic systems
Other keywords: robust H2 sliding mode control; equality constraint; discrete-time switching function; H2 performance constraints; uncertain systems; linear matrix inequalities; nonlinear discrete-time stochastic systems; exponentially mean-square stability
Subjects: Nonlinear control systems; Stability in control theory; Algebra; Time-varying control systems; Optimal control; Multivariable control systems; Discrete control systems
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