A new sufficient condition for arbitrary pole placement by real constant output feedback

Leventides, John; Karcanias, N.

doi:10.1016/0167-6911(92)90005-d

Cited by 17 publications

(19 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…whenever Mll is invertible, we get (9) which is the same as the formula in the statement of the lemma. [] From (9), one easily determines the coefficient of s" in the unnormalized closed-loop characteristic polynomial:…”

Section: Lemma2 Let a System (Abc) Be Given And Write G(s) := C(smentioning

confidence: 48%

“…[] From (9), one easily determines the coefficient of s" in the unnormalized closed-loop characteristic polynomial:…”

Section: Lemma2 Let a System (Abc) Be Given And Write G(s) := C(smentioning

confidence: 99%

“…During the eighties there were numerous papers which showed that Kimura's bound could be improved, and we refer to [3,9,11] and in particular to the survey article of Byrnes [4] where also more complete references can be found.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generic eigenvalue assignment by memoryless real output feedback

Rosenthal

Schumacher

Willems

1995

Systems & Control Letters

View full text Add to dashboard Cite

show abstract

Section: Lemma2 Let a System (Abc) Be Given And Write G(s) := C(smentioning

confidence: 48%

“…[] From (9), one easily determines the coefficient of s" in the unnormalized closed-loop characteristic polynomial:…”

Section: Lemma2 Let a System (Abc) Be Given And Write G(s) := C(smentioning

confidence: 99%

See 1 more Smart Citation

Generic eigenvalue assignment by memoryless real output feedback

Rosenthal

Schumacher

Willems

1995

Systems & Control Letters

View full text Add to dashboard Cite

show abstract

“…The first of the two problems naturally belongs to the intersection theory of complex algebraic varieties, whereas, the latter belongs to the intersection theory of semi-algebraic sets. Determining real intersections is not an easy problem (Leventides and Karcanias, 1992); furthermore, it is also important to be able to compute solutions whenever such solutions exist and define "approximate solutions" when exact solutions do not exist. The use of algebraic Geometry in the study of spectrum assignment problems was originally introduced in Hermann, and Martin (1975), Brockett, and Byrnes, (1981), where an affine space approach has been used.…”

Section: Introductionmentioning

confidence: 99%

“…The approach heavily relies on exterior algebra and this has implications on the computability of solutions (reconstruction of solutions whenever they exist) and introduces new sets of invariants (of a projective character) which, in turn, characterise the solvability of the problem. This approach has been further developed in Karcanias, (1995), (1998)) by the development of a "blow-up" methodology for linearization of multi-linear maps that permit the development of computations, as well as techniques for establishing the development of real solutions (Leventides and Karcanias, (1992)). The distinct advantages of the DAP approach, which is a projective space approach, are: it provides the means for computing the solutions; it can handle both generic and exact solvability investigations, and it introduces new criteria for the characterisation of solvability of different problems.…”

Section: Introductionmentioning

confidence: 99%

Generalised resultants, dynamic polynomial combinants and the minimal design problem

Karcanias

2013

International Journal of Control

Self Cite

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThe theory of dynamic polynomial combinants is linked to the linear part of the Dynamic Determinantal Assignment Problems (DAP), which provides the unifying description of the dynamic, as well as static pole and zero dynamic assignment problems in Linear Systems. The assignability of spectrum of polynomial combinants provides necessary conditions for solution of the original DAP. This paper deals demonstrates the origin of dynamic polynomial combinants from Linear Systems examines issues of their representation, the parameterization of dynamic polynomial combinants according to the notions of order and degree and examines the spectral assignment of them. Central to this study is the link of dynamic combinants to the theory of "Generalised Resultants", which provide the matrix representation of the dynamic combinants. The paper considers the case of coprime set polynomials for which spectral assignability is always feasible and provides a complete characterisation of all assignable combinants with order above and below the Sylvester order. A complete parameterization of combinants and respective Generalised Resultants is given and this leads naturally to the characterisation of the minimal degree and order combinant for which spectrum assignability may be achieved, which is referred to as the "Dynamic Combinant Minimal Design" (DCMD)problem. An algorithmic approach based on rank tests of Sylvester matrices is given which produces the minimal order and degree solution in a finite number of steps. Such solutions provide low bounds for the respective Dynamic Assignment control problems.

show abstract

Arbitrary Pole Placement by Constant Output Feedback for Linear Time Invariant Systems

Kiritsis

2016

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

A new sufficient condition for arbitrary pole placement by real constant output feedback

Cited by 17 publications

References 10 publications

Generic eigenvalue assignment by memoryless real output feedback

Generic eigenvalue assignment by memoryless real output feedback

Generalised resultants, dynamic polynomial combinants and the minimal design problem

Arbitrary Pole Placement by Constant Output Feedback for Linear Time Invariant Systems

Contact Info

Product

Resources

About