Partial Strong Structural Controllability

TL;DR

This paper introduces partial strong structural controllability (PSSC), a new controllability concept that extends existing notions by considering fixed zero, generic, and unspecified entries in system matrices, with algebraic and graph-theoretic conditions.

Contribution

It defines PSSC, provides necessary and sufficient conditions for single-input systems, and connects these results to a maximum matching criterion for strong structural controllability.

Findings

PSSC generalizes strong structural controllability.

Algebraic and graph-theoretic conditions for PSSC are established.

A new maximum matching criterion for SSC is derived.

Abstract

This paper introduces a new controllability notion, termed partial strong structural controllability (PSSC), on a structured system whose entries of system matrices are either fixed zero or indeterminate, which naturally extends the conventional strong structural controllability (SSC) and bridges the gap between structural controllability and SSC. Dividing the indeterminate entries into two categories, generic entries and unspecified entries, a system is PSSC, if for almost all values of the generic entries in the parameter space except for a set of measure zero, and any nonzero (complex) values of the unspecified entries, the corresponding system is controllable. We highlight that this notion generalizes the generic property embedded in the conventional structural controllability for single-input systems. We then give algebraic and (bipartite) graph-theoretic necessary and sufficient conditions for single-input systems to be PSSC. Conditions for multi-input systems are subsequently given for a special case. It is shown the established results can induce a new maximum matching based criterion for SSC over the system bipartite graph representations.