2017/08/26 by Bin Zhou, Zhou, Bin · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Matrix Theory and Algorithms #Quantum chaos and dynamical systems #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1708.07947
openalex publication_date 2017/08/26 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28
We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly, can be used to model second-order linear systems in a very dense manner. These linear bimatrix equations include generalized Sylvester bimatrix equations, Sylvester bimatrix equations, Stein bimatrix equations, and Lyapunov bimatrix equations. Complete and explicit solutions are provided in terms of the bimatrices that are coefficients of the equations/systems. The obtained solutions are then used to solve the full state feedback pole assignment problem for complex-valued linear system. For a special case of complex-valued linear systems, the so-called antilinear system, the solutions are also used to solve the so-called anti-preserving (the closed-loop system is still an antilinear system) and normalization (the closed-loop system is a normal linear system) problems. Second-order linear systems, particularly, the spacecraft rendezvous control system, are used to demonstrate the obtained theoretical results.