Local controllability and minimum energy control of continuous 2-D linear time-invariant system (Q1360047)

Linear, continuous-time, 2-D systems described by partial differential equations with constant coefficients are considered. Using a general response formula, a necessary and sufficient condition for local controllability in a given rectangle is formulated and proved. This condition requires verification of the rank of a suitably defined controllability matrix and has a pure algebraic form. Moreover, the minimum energy control problem for the considered systems is formulated and effectively solved under a local controllability condition. An analytic solution of the minimum energy control problem is given using the controllability matrix. Finally, concluding remarks and comments on controllability and the minimum energy control problem for 2-D systems are presented. The results of the paper extend to continuous 2-D linear systems theorems, which have been known for discrete 2-D linear systems [\textit{J. Klamka}, Controllability of dynamical systems, Kluwer Academic Publishers, Dordrecht (1991; Zbl 0732.93008), Chapter 2].