Modal Strong Structural Controllability: Graph-Based Analysis in LTI Systems

• 成果类型: Article
• 署名作者: Mousavi, Shima Sadat
• 署名单位: California Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3568561
• 发表日期: 2025
• 关键词: ZERO FORCING SETS; SIGN CONTROLLABILITY; MINIMUM RANK

摘要

In this article, we introduce a new concept of modal strong structural controllability in linear time-invariant (LTI) systems. An eigenvalue of a system matrix is considered controllable if it can be directly influenced by the control inputs. We focus on an arbitrary set Delta subset of C and define a specific family of systems as modal strongly structurally controllable with respect to Delta if, for all systems in this family, every lambda is an element of Delta is a controllable eigenvalue. In this family of LTI systems, the zero/nonzero/arbitrary pattern of system matrices is known, along with additional information about the spectrum of the subsystems, derived from their physical properties. To establish controllability conditions, we define a Delta-graph and use a coloring process to relate the set of control subsystems to zero forcing sets. We define efficient Delta, and for networks of 1-D subsystems, we prove that the graph-theoretic condition is both necessary and sufficient when Delta is efficient. Moreover, for cases where Delta is not efficient, we establish conditions under which it can be partitioned into efficient subsets. Furthermore, we demonstrate how our approach can derive existing results on strong structural controllability when Delta={0} or Delta=C\{0}.