Enhanced LMI representations for H2 performance of polytopic uncertain systems: Continuous-time case

Wu, Ai‐Guo; Duan, Guang‐Ren

doi:10.1007/s11633-006-0304-5

Cited by 9 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(Proof of the first part) Suppose there are matrices P11τ > 0, P22τ > 0, P12τ , Xτ , Rτ , Uτ , A f τ , B f τ , C f τ , and scalars λ1, λ2 satisfying (13).…”

Section: Theorem 1 Filtering Error Systemmentioning

confidence: 99%

See 1 more Smart Citation

Improved parameter-dependent H ∞ filtering for polytopic Delta operator systems

Yao

Zhang

2009

Int. J. Autom. Comput.

View full text Add to dashboard Cite

The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads to a less conservative result than conventional design methods. A numerical example is given to illustrate the effectiveness of the proposed approach.

show abstract

“…(Proof of the first part) Suppose there are matrices P11τ > 0, P22τ > 0, P12τ , Xτ , Rτ , Uτ , A f τ , B f τ , C f τ , and scalars λ1, λ2 satisfying (13).…”

Section: Theorem 1 Filtering Error Systemmentioning

confidence: 99%

“…By Theorems 1 and 2, an admissible parameterdependent H∞ filter in the form of (3) exists if there exist function matrices P11τ > 0, P22τ > 0, P12τ , Xτ , Rτ , Uτ , A f τ , B f τ , C f τ , and scalars λ1, λ2 satisfying (13). Now, assume that the above function matrices are of the following form…”

Section: Introduce Matricesmentioning

confidence: 99%

Improved parameter-dependent H ∞ filtering for polytopic Delta operator systems

Yao

Zhang

2009

Int. J. Autom. Comput.

View full text Add to dashboard Cite

show abstract

“…The generalized ratio control principle is reformulated as the full-state feedback control with one equality constraint. Solving this problem, the technique for an enhanced BRL representation [20,21] is exploited, to circumvent potentially ill-conditioned singular task concerning the discrete-time systems control design with state equality constraints [22]. Due to application of the enhanced BRL, which decouple the Lyapunov matrix and the system matrices, the design task stays well-conditioned.…”

Section: Introductionmentioning

confidence: 99%

Generalized Ratio Control of Discrete-Time Systems

Krokavec¹,

Filasová²

2017

Dynamical Systems - Analytical and Computational Techniques

View full text Add to dashboard Cite

This chapter exposes the important connection between ratio control and the state control reflecting equality constraint for linear discrete-time systems, which allows significant reduction in computational complexity and efforts. Based on an enhanced bounded real lemma form, to outperform known approaches, the existence of the state feedback for such defined singular task is proven, and the design procedure based on the linear matrix inequalities is provided. The proposed principle, guaranteeing feasibility of the set of inequalities, improves steady-state accuracy of the ratio control and essentially reduces the design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated.

show abstract

“…To include these requirements the equivalent LMI representations of 16 www.intechopen.com BRL for continuous-time, as well as discrete-time uncertain systems were introduced (e.g. see Wu and Duan (2006), and Xie (2008)). Motivated by the underlying ideas a simple technique for the BRL representation can be extended to state feedback controller design, performing system H ∞ properties of quadratic performance.…”

Section: Introductionmentioning

confidence: 99%