arXiv subjects

Shun-Pin Hsu

Publications and source records attributed to Shun-Pin Hsu.

5 recordsLinked to original sources

arXiv2026

Sarymsakov-Type Semigroups With Support Dominance and Nested Mixing Cores

This note develops three multiplication-closed families of stochastic matrices for consensus under arbitrary switching. The first is a support-dominance enlargement of an earlier power-generated construction, in which exact support-pattern matching is relaxed to a dominance-type condition without losing closure under multiplication. The second is a fixed-core class with an exact uniform scrambling horizon and corresponding convergence-rate guarantees for switching products. The third and main contribution is the almost Sarymsakov class, obtained by allowing variable mixing-core dimensions under suitable structural conditions. This new semigroup class properly contains the classical Sarymsakov class and admits a dimension-only scrambling-horizon bound. Examples illustrate the necessity of the proposed structural assumptions and clarify the sharpness or limitations of the derived bounds.

math.DS↗

arXiv2019

Generalizing Laplacian Controllability of Paths

It is well known that if a network topology is a path or line and the states of vertices or nodes evolve according to the consensus policy, then the network is Laplacian controllable by an input connected to its terminal vertex. In this work a path is regarded as the resulting graph after interconnecting a finite number of two-vertex antiregular graphs and then possibly connecting one more vertex. It is shown that the single-input Laplacian controllability of a path can be extended to the case of interconnecting a finite number of $k$-vertex antiregular graphs with or without one more vertex appended, for any positive integer $k$. The methods to interconnect these antiregular graphs and to select the vertex for connecting the single input that renders the network Laplacian controllable are presented as well.

math.OC↗

arXiv2018

Laplacian Controllability of Interconnected Graphs

In this work we consider the Laplacian controllability of a graph constructed by interconnecting a finite number of single-input Laplacian controllable graphs. We first study the interconnection realized by the composite graph of two connected simple graphs called the structure graph and the cell graph. Suppose the cell graph is Laplacian controllable by an input connected to some special vertex called the composite vertex. The composite graph is constructed by interconnecting all cell graphs through the composite vertices which alone form the structure graph. We then show that the structure graph is Laplacian controllable by an input connected to some vertex of the graph if and only if the composite graph is Laplacian controllable by that input connected to that composite vertex. In the second part of the paper, we view a path as a graph generated by interconnecting a finite number of two-vertex antiregular graph, and possibly connected to a one-vertex path, where the two vertices of the antiregular graph are interpreted as the terminal vertex (or the dominating vertex) and the degree-repeating vertex. We show that with a similar connecting scheme the single-input Laplacian controllability is preserved if we increase the number of vertices of the antiregular graph and that of the path. Numerical examples are presented to illustrate our results.

math.OC↗

arXiv2018

Laplacian Controllability of Threshold Graphs

This paper is concerned with the controllability problem of a connected threshold graph following the Laplacian dynamics. An algorithm is proposed to generate a spanning set of orthogonal Laplacian eigenvectors of the graph from a straightforward computation on its Laplacian matrix. A necessary and sufficient condition for the graph to be Laplacian controllable is then proposed. The condition suggests that the minimum number of controllers to render a connected threshold graph controllable is the maximum multiplicity of entries in the conjugate of the degree sequence determining the graph, and this minimum can be achieved by a binary control matrix. The second part of the work is the introduction of a novel class of single-input controllable graphs, which is constructed by connecting two antiregular graphs with almost the same size. This new connecting structure reduces the sum of the maximum vertex degree and the diameter by almost one half, compared to other well-known single-input controllable graphs such as the path and the antiregular graph, and has potential applications in the design of controllable graphs subject to practical edge constraints. Examples are provided to illustrate our results.

math.OC↗

arXiv2016

Time response of a scalar dynamical system with multiple delays via Lambert W functions

In this work, we establish the response of scalar systems with multiple discrete delays based on the Laplace transform. The time response function is expressed as the sum of infinite series of exponentials acting on eigenvalues inside countable branches of the Lambert W functions. Eigenvalues in each branch of Lambert W function are computed by a numerical iteration. Numerical examples are presented to illustrate the results obtained.

math.DS↗