289 research outputs found
Eigenvalue Comparisons for Second-Order Linear Equations with Boundary Value Conditions on Time Scales
This paper studies the eigenvalue comparisons for second-order linear equations with boundary conditions on time scales. Using results from matrix algebras, the existence and comparison results concerning eigenvalues are obtained
Observer-based Leader-following Consensus for Positive Multi-agent Systems Over Time-varying Graphs
This paper addresses the leader-following consensus problem for discrete-time
positive multi-agent systems over time-varying graphs. We assume that the
followers may have mutually different positive dynamics which can also be
different from the leader. Compared with most existing positive consensus works
for homogeneous multi-agent systems, the formulated problem is more general and
challenging due to the interplay between the positivity requirement and
high-order heterogeneous dynamics. To solve the problem, we present an extended
version of existing observer-based design for positive multi-agent systems. By
virtue of the common quadratic Lyapunov function technique, we show the
followers will maintain their state variables in the positive orthant and
finally achieve an output consensus specified by the leader. A numerical
example is used to verify the efficacy of our algorithms
Multilevel Matrix Factor Model
Large-scale matrix data has been widely discovered and continuously studied
in various fields recently. Considering the multi-level factor structure and
utilizing the matrix structure, we propose a multilevel matrix factor model
with both global and local factors. The global factors can affect all matrix
times series, whereas the local factors are only allow to affect within each
specific matrix time series. The estimation procedures can consistently
estimate the factor loadings and determine the number of factors. We establish
the asymptotic properties of the estimators. The simulation is presented to
illustrate the performance of the proposed estimation method. We utilize the
model to analyze eight indicators across 200 stocks from ten distinct
industries, demonstrating the empirical utility of our proposed approach.Comment: 47 pages, 22 figure
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