Strictly Totally Positive Systems

Carnicer, J. M.; Peña, J. M.; Zalik, R. A.

doi:10.1006/jath.1997.3132

Cited by 41 publications

(14 citation statements)

References 22 publications

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“…. , γ d )) forms a Chebyshev system, 2 which is an important notion in approximation theory, theory of finite moments, and other areas-see, e.g., [KS66,CPZ98]. Conversely, every Chebyshev system (γ 0 , .…”

Section: Introductionmentioning

confidence: 99%

Curves in $\mathbb R^d$ intersecting every hyperplane at most $d+1$ times

Bárány¹,

Matoušek²,

Pór³

2016

J. Eur. Math. Soc.

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By a curve in R d we mean a continuous map γ : I → R d , where I ⊂ R is a closed interval. We call a curve γ in R d (≤ k)-crossing if it intersects every hyperplane at most k times (counted with multiplicity). The (≤ d)-crossing curves in R d are often called convex curves and they form an important class; a primary example is the moment curve {(t, t 2 , . . . , t d ) : t ∈ [0, 1]}. They are also closely related to Chebyshev systems, which is a notion of considerable importance, e.g., in approximation theory. Our main result is that for every d there is M = M (d) such that every (≤ d + 1)-crossing curve in R d can be subdivided into at most M (≤ d)-crossing curve segments. As a consequence, based on the work of Eliáš, Roldán, Safernová, and the second author, we obtain an essentially tight lower bound for a geometric Ramsey-type problem in R d concerning order-type homogeneous sequences of points, investigated in several previous papers.

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Section: Introductionmentioning

confidence: 99%

Curves in $\mathbb R^d$ intersecting every hyperplane at most $d+1$ times

Bárány¹,

Matoušek²,

Pór³

2016

J. Eur. Math. Soc.

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“…In the same manner, the MIMO Luenberger observer, associated with the observable system (1), (2), is given as …”

Section: Strictly Positive Mimo Systemsmentioning

confidence: 99%

“…The mathematical theory of Metzler matrices has a close relationship to the theory of positive linear time-invariant (LTI) dynamical systems, since in the state-space description form the system dynamics matrix of a positive systems is Metzler and the system input and output matrices are nonnegative matrices. Other references can find, e.g., in [2], [3], [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of discrete-time LTI positive systems

Krokavec

Filasová

2017

Archives of Control Sciences

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The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the statefeedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

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“…For instance, it is well known that B-splines collocation matrices are totally positive, and some recent papers [6,7] have shown the strong relationship between Tchebycheff and weak Tchebycheff systems and totally positive systems. Totally positive bases have also been found for the generalized spline spaces of [12,20], for the L-splines space (see [15]), and for the Tchebycheffian splines space (see [19,Chap.…”

Section: Introductionmentioning

confidence: 98%