[Hamiltonian (script capital H)]∞ mode reduction for two-dimensional discrete state-delayed systems

Wu, Ligang; Shi, Peng; Gao, Huijun; Wang, C

doi:10.1049/ip-vis:20050372

Cited by 25 publications

(15 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another approach to the model approximation synthesis depends heavily upon the celebrated elimination/projection lemma, which casts the model approximation problem into some LMI conditions plus equality constraints Wu et al (2006); Wu and Zheng (2009). However, it is worth pointing out that due to the imperfect mode information in 2-D MJLSs, the indices m ∈ I, n ∈ I (m) UK , and s = 1, 2, .…”

Section: Model Approximation Via Iterative Approachmentioning

confidence: 99%

“…Thus, the so-called projection approach Wu et al (2006); Wu and Zheng (2009) can not be utilized to derive the approximation model gains in (9). In other words, for the 2-D MJLS in (1) with imperfect mode information, the approximation model (5) can not be obtained by the projection approach as proposed in Wu et al (2006); Wu and Zheng (2009). Alternatively, in this subsection we may resort to a direct approach to separate the Lyapunov matrices from the system matrices.…”

Section: Model Approximation Via Iterative Approachmentioning

confidence: 99%

“…Model approximation/reduction thus plays an important role in the process of control system design. During the past few decades, various efficient model approximation schemes have been proposed, involving the Hankel norm approximation method Zhou (1995); Gao et al (2004), the H 2 approach Yan and Lam (1999), the H ∞ approach Zhang et al (2003); ; Wu et al (2006); Gao et al (2006); Wu and Zheng (2009) and the L 2 -L ∞ approach Lam et al (2005). More recently, the linear matrix inequality (LMI) technique has been applied to deal with the model approximation problem for different classes of systems Zhang et al (2003); Wu and Zheng (2009);Lam et al (2005).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information

Wei

Qiu

Karimi

et al. 2014

Multidim Syst Sign Process

View full text Add to dashboard Cite

This paper is concerned with the problem of H ∞ model approximation for a class of two-dimensional (2-D) discrete-time Markovian jump linear systems with state-delays and imperfect mode information. The 2-D system is described by the well-known FornasiniMarchesini local state-space model, and the imperfect mode information in the Markov chain simultaneously involves the exactly known, partially unknown and uncertain transition probabilities. By using the characteristics of the transition probability matrices, together with the convexification of uncertain domains, a new H ∞ performance analysis criterion for the underlying system is firstly derived, and then two approaches, namely, the convex linearisation approach and iterative approach, to the H ∞ model approximation synthesis are developed. The solutions to the problem are formulated in terms of strict linear matrix inequalities (LMIs) or a sequential minimization problem subject to LMI constraints. Finally, simulation studies are provided to illustrate the effectiveness of the proposed design methods.

show abstract

Section: Model Approximation Via Iterative Approachmentioning

confidence: 99%

Section: Model Approximation Via Iterative Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information

Wei

Qiu

Karimi

et al. 2014

Multidim Syst Sign Process

View full text Add to dashboard Cite

show abstract

“…Furthermore, the delay-dependent control system matrices A ck , A ckd , B ck (k = 1, 2), C c and D c can be derived from equation (29), i.e., the delay-dependent H ∞ control problem for system (19)- (21) is solved.…”

Section: Theorem 3 We Are Given Scalars T T 1 and T 2 2-d State-dementioning

confidence: 99%

“…These applications provide a rich engineering physical background for 2-D system theory. When controlling a real plant, it is also desirable to design a control system which is not only stable, but also guarantees an adequate level of performance, such as H ∞ control [3], guaranteed cost control [7] and H ∞ mode reduction [19], for 2-D discrete systems.…”

Section: Introductionmentioning

confidence: 99%

Output Feedback H ∞ Control for 2-D State-Delayed Systems

Peng

Guan

2008

Circuits Syst Signal Process

View full text Add to dashboard Cite

In this paper, we consider a class of two-dimensional (2-D) local statespace (LSS) Fornasini-Marchesini (FM) second models with delays in the states, and we study delay-independent and delay-dependent H ∞ control problems via output feedback. First, based on the definition of H ∞ disturbance attenuation γ for 2-D state-delayed systems, we propose a delay-dependent bounded real lemma. Specifically, a new Lyapunov functional candidate is introduced and free-weighting matrices are added to the difference Lyapunov functional for 2-D systems possessing two directions. Then delay-independent and delay-dependent output feedback H ∞ controllers are developed that ensure that the closed-loop system is asymptotically stable and has H ∞ performance γ in terms of linear matrix inequality (LMI) feasibility. Furthermore, the minimum H ∞ norm bound γ is obtained by solving linear objective optimization problems. Numerical examples demonstrate the effectiveness and advantages of the LMI approach to H ∞ control problems for 2-D state-delayed systems.

show abstract

On stability and stabilizability of positive delay systems

Lam

Shu

et al. 2009

Asian Journal of Control

View full text Add to dashboard Cite

The stabilization problem with positivity is investigated in this note for discrete-time linear systems with time delay. A delay-independent necessary and sufficient condition is proposed in terms of linear matrix inequalities (LMIs) for the existence of desired controllers that guarantee the closed-loop system to be asymptotically stable and positive. In addition, the obtained result is further extended to more general case when the system matrices contain uncertain parameters, where a sufficient condition is obtained. The frequently used polytopic parameter uncertainty is taken into consideration. Since the conditions obtained are expressed as LMIs, which can be easily verified by using standard numerical software. A numerical example is provided to illustrate the proposed results.

show abstract

[Hamiltonian (script capital H)]∞ mode reduction for two-dimensional discrete state-delayed systems

Cited by 25 publications

References 18 publications

Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information

Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information

Output Feedback H ∞ Control for 2-D State-Delayed Systems

On stability and stabilizability of positive delay systems

Contact Info

Product

Resources

About