Stability Radii of Interconnected Positive Systems with Uncertain Couplings

2009 ◽  
pp. 71-81
Author(s):  
Diederich Hinrichsen
Keyword(s):  
Positive Systems ◽  
Stability Radii

scholarly journals The Robustness of Strong Stability of Positive Homogeneous Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
The Anh Bui ◽  
Dang Xuan Thanh Duong
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Strong Stability ◽  
Positive Systems ◽  
Stability Radii

We study the robustness of strong stability of the homogeneous difference equation via the concept of strong stability radii: complex, real and positive radii in this paper. We also show that in the case of positive systems, these radii coincide. Finally, a simple example is given.

scholarly journals Balanced truncation of k-positive systems

2021 ◽  
pp. 1-1
Author(s):  
Christian Grussler ◽  
Tobias Damm ◽  
Rodolphe Sepulchre
Keyword(s):  
Balanced Truncation ◽  
Positive Systems

scholarly journals On the similarity to nonnegative and Metzler Hessenberg forms

2021 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Christian Grussler ◽  
Anders Rantzer
Keyword(s):  
Standard Form ◽  
Complete Characterization ◽  
Nonnegative Matrices ◽  
Positive Systems ◽  
Third Order ◽  
Hessenberg Form ◽  
Hessenberg Matrices ◽  
Open Question ◽  
Order Continuous

Abstract We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions n 3, there always exists a subset of nonnegative matrices that are not similar to a nonnegative Hessenberg form, which in case of n = 3 also provides a complete characterization of all such matrices. For Metzler matrices, we further establish that they are similar to Metzler Hessenberg matrices if n 4. In particular, this provides the first standard form for controllable third order continuous-time positive systems via a positive controller-Hessenberg form. Finally, we present an example which illustrates why this result is not easily transferred to discrete-time positive systems. While many of our supplementary results are proven in general, it remains an open question if Metzler matrices of dimensions n 5 remain similar to Metzler Hessenberg matrices.

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