Controllability of linear and semilinear control systems
Bull. Korean Math. Soc. 2000 Vol. 37, No. 2, 361-376
Jin-Mun Jeong, Jong-Yeoul Park, and Chul-Yun Park
Pukyong National University, Pusan National University, Pukyong National University
Abstract : Our purpose is to seek that the reachable set of the semilinear system $\frac{d}{dt}x(t) = A x(t) + f(t, x(t)) + B u(t)$ is equivalent to that of its corresponding to linear system(the case where $f=0$). Under the assumption that the system of generalized eigenspaces of $A$ is complete, we will show that the reachable set corresponding to the linear system is independent of $t$ in case $A$ generates $C_0$-semigroup. An illustrative example for retarded system with time delay is given in the last section.
Keywords : semilinear evolution equation, reachable sets approximate controllability, generalized eigenspaces
MSC numbers : Primary 35B37; Secondary 93C20
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