Pole placement with minimised norm controllers

Kouvaritakis, B.; Cameron, R.G.

doi:10.1049/ip-d.1980.0005

Cited by 12 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2) What is the maximum number of vectors X which can satisfy (2), and when do fewer than the maximum number occur?…”

Section: Research Problemmentioning

confidence: 99%

See 1 more Smart Citation

Research problem

1983

Linear and Multilinear Algebra

View full text Add to dashboard Cite

“…(2) What is the maximum number of vectors X which can satisfy (2), and when do fewer than the maximum number occur?…”

Section: Research Problemmentioning

confidence: 99%

“…The problem originally arose in attempts to design control systems with minimum norm feedback matrices [2,3], but it has also occurred in the study of the stability of multivariable nonlinear feedback systems [4].…”

Section: Research Problemmentioning

confidence: 99%

Research problem

1983

Linear and Multilinear Algebra

View full text Add to dashboard Cite

“…In this way, O'Reilly and Fahmy (1985) have specified the minimum number of free parameters and shown that a general eigenvalue assignment control is achieved by state-feedback controller. Kouvaritakis and Cameron (1980), Cameron (1988) and Varga (2000) have presented methods with minimised norm feedback matrix. The parametrisation of controllers in the eigenvalue assignment problem has also been performed using modal control approach (Saif 1989;Roppenecker 1996) and state transition graph (Katayama and Ichikawa 1992).…”

Section: Introductionmentioning

confidence: 98%

Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems

Ataei

Enshaee

2011

International Journal of Control

View full text Add to dashboard Cite

In this article, an improved method for eigenvalue assignment via state feedback in the linear time-invariant multivariable systems is proposed. This method is based on elementary similarity operations, and involves mainly utilisation of vector companion forms, and thus is very simple and easy to implement on a digital computer. In addition to the controllable systems, the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs. Moreover, two types of state-feedback gain matrices can be achieved by this method: (1) the numerical one, which is unique, and (2) the parametric one, in which its parameters are determined in order to achieve a gain matrix with minimum Frobenius norm. The numerical examples are presented to demonstrate the advantages of the proposed method.

show abstract

“…For multi-input systems such an F is non-unique (Wonham, 1974) and several algorithms (e.g. see Chu, 2001;Kautsky, Nichols, & Dooren, 1985;Mehrmann & Xu, 1997;Miminis & Paige, 1982;Tam & Lam, 1997;Varga, 2000aVarga, , 2000b, and references therein) optimise various aspects of the F matrix and associated quantities based on the degrees of freedom available in F. It was shown in Mehrmann and Xu (1997) that relevant quantities for such optimisation formulations are the state feedback matrix norm (Keel, Fleming, & Bhattacharyya, 1985;Kouvaritakis & Cameron, 1980;Varga, 2000aVarga, , 2000bWang & Chow, 2000), the condition number of the associated eigenvector matrix (Chu, 2001;Kautsky et al, 1985;Mehrmann & Xu, 1997;Miminis & Paige, 1982;Rami, Faiz, Benzaouia, & Tadeo, 2009;Tam & Lam, 1997;Tits & Yang, 1996;Varga, 2000aVarga, , 2000b and the distance to uncontrollability (Mehrmann & Xu, 1997). These optimisation problems are rarely convex and have varying numerical properties (Rami et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

Feedback norm minimisation with regional pole placement

Datta

Chakraborty

2014

International Journal of Control

View full text Add to dashboard Cite

This article proposes a convex algorithm for minimising an upper bound of the state feedback gain matrix norm with regional pole placement for linear time-invariant multi-input systems. The inherent non-convexity in this optimisation is resolved by a combination of two separate approaches: (1) an inner convex approximation of the polynomial matrix stability region due to Henrion and (2) a novel convex parameterisation of column reduced matrix fraction system representations. Using a sequence of approximations enabled by the above two methods, it is shown that the constraints on closed-loop poles (both pre-specified exact locations and regional placement) define linear matrix inequalities. Finally, the effectiveness of the proposed algorithm is compared with similar pole placement algorithms through numerical examples.

show abstract

Pole placement with minimised norm controllers

Cited by 12 publications

References 0 publications

Research problem

Research problem

Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems

Feedback norm minimisation with regional pole placement

Contact Info

Product

Resources

About