Controllability for a class of parallelly connected polynomial systems (Q1306788)

Linear and nonlinear finite-dimensional, time-invariant and discrete-time control systems are considered. The main purpose of the paper is to study null controllability and complete controllability of a class of linear subsystems connected in parallel. Using algebraic methods, necessary and sufficient conditions for null and complete controllability are formulated and proved. The controllability tests require verification of controllability of the subsystems. Similarly, null and complete controllability conditions for continuous-time versions are also derived. Several special cases are also considered. Moreover, remarks and comments on controllability problems for discrete-time control systems are presented. Similar controllability problems have been recently discussed in the paper [\textit{D. Nešić} and \textit{I. M. Y. Mareels}, ``Dead beat controllability of polynomial systems: symbolic computation approaches'', IEEE Trans. Autom. Control 43, No. 2, 162-175 (1998; Zbl 0907.93038)].