On the positive orthant controllability of two-dimensional bilinear systems
In the paper complete controllability on the positive orthant \(M=\{x\in R^ 2:x_ 1>0,\quad x_ 2>0\}\) of two-dimensional stationary bilinar control systems \[ \dot x(t)=(A+u(t)B)x(t),\quad x(t)\in M \] is considered. It is assumed, that the 2\(\times 2\) matrix A is essentially positive, that is \(a_{12}>0\), \(a_{21}>0\), and moreover, B is a 2\(\times 2\) diagonal matrix with nonzero diagonal elements \(b_ 1\neq 0,b_ 2\neq 0.\) Using the general results formulated in a paper of \textit{W. M. Boothby} [SIAM J. Control Optimization 20, 634-644 (1982; Zbl 0488.93009)], sufficient and necessary conditions for complete controllability on the positive orthant M are presented. Some additional comments concerning more general multi-dimensional bilinear stationary control systems are also given.
scientific article; zbMATH DE number 3845421
scientific article