Robustness analysis in the delta-domain using fixed-structure multipliers

Collins, Emmanuel G.; Haddad, Wassim M.; Chellaboina, VijaySekhar; Song, Tinglun

doi:10.1109/cdc.1997.652352

Cited by 15 publications

(9 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where P = P q h. Introducing this result in (6) and (9), we obtain the following result. Lemma 3: The solution P q > 0 to the LMI F q (P q , γ) > 0 for the system G q (3) can alternatively be obtained as…”

Section: Relation Between Shift and Delta Operator Lmismentioning

confidence: 78%

See 1 more Smart Citation

Numerical sensitivity of Linear Matrix Inequalities for shorter sampling periods

Lennartson

Middleton

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Abstract-The numerical sensitivity of Linear Matrix Inequalities (LMIs) arising in the H∞ norm computation in discrete time is analyzed. Rapid sampling scenarios are examined comparing both shift and delta operator formulations of the equations. The shift operator formulation is shown in general to be arbitrarily poorly conditioned as the sampling rate increases. The delta operator formulation includes both recentering (to avoid cancellation problems ) and rescaling, and avoids these difficulties. However, it is also shown that rescaling of the shift operator formulation gives substantial improvements in numerical conditioning, whilst recentering is of more limited benefit.

show abstract

Section: Relation Between Shift and Delta Operator Lmismentioning

confidence: 78%

“…These sensitivity issues are related to scaling and cancellation, two well know numerical problems for shift operator models that are conveniently solved using the delta operator [5]. More recently, delta operator based LMIs have been introduced, often related to H ∞ robust control problems [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Numerical sensitivity of Linear Matrix Inequalities for shorter sampling periods

Lennartson

Middleton

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…In this section, an over bound on the Cl performance functional (29) will be developed over the entire uncertainty set for an uncertain system by using the Popov-Tsypkin multiplier [2]. The upper bound to be developed ran be used in the synthesis of robust f?, estimators.…”

Section: Bounds On Performance Over the Uncertainty Set Via Multipliementioning

confidence: 99%

“…The Robust el Estimation ProblemConsider the discrete-time, linear uncertain system xp(k + 1) = (Ap + AA&,@) + ~o o , l~o o (~) , (C, + ACP)ZP@) + L , 2 % 0 ( k )(2) …”

mentioning

confidence: 99%

See 1 more Smart Citation

Robust l/sub 1/ estimation using the Popov-Tsypkin multiplier with application to robust fault detection

Collins

Song²

1999

Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)

View full text Add to dashboard Cite

This paper considers the design of robust e 1 estimators based on multiplier theory (which is intimately related to mixed st.ructured singula,r value theory) and the applica-t~ioii of robust. tl est,imators to robust fault detection. The key to wtinintor-based, robust fault detection is to generat.e resitlnals which are robust aga.inst pla.nt uncertainties and cstenial dist,urbance inputs, which in turn requires the tlesigii of robust estimators. Specifically, the Popov-Tsppkin multiplier is used to develop an upper bound on an f 1 cost fiinct,ion over an uncertainty set. The robust tl estiniat.ion problem is formulated a.s a parameter optimization problem in which the upper bound is minimized siiljjwt to a Riccati equation constra,int. The estimation algoritliiii has t,wo stages. The first stage solves a mixed-~ioriu H 2 / f , estimation problem. In the second stage the f l estimator is made robust. The robust Cl estimation framcwork is then applied to robust fault detection of dyiianiic: systems.

show abstract

A J-lossless coprime factorisation approach to H∞ control in delta domain

Suchomski

2002

Automatica

View full text Add to dashboard Cite

Robustness analysis in the delta-domain using fixed-structure multipliers

Cited by 15 publications

References 10 publications

Numerical sensitivity of Linear Matrix Inequalities for shorter sampling periods

Numerical sensitivity of Linear Matrix Inequalities for shorter sampling periods

Robust l/sub 1/ estimation using the Popov-Tsypkin multiplier with application to robust fault detection

A J-lossless coprime factorisation approach to H∞ control in delta domain

Contact Info

Product

Resources

About