CONTROLLABILITY OF LINEAR AND SEMILINEAR CONTROL SYSTEMS

• Jeong, Jin-Mun (Division of Mathematical Sciences, Pukyong National University) ;
• Park, Jong-Yeoul (Department of Mathematics, Pusan National University) ;
• Park, Chul-Yun (Division of Mathematical Sciences Pukyong National University)
• Published : 2000.05.01
• 42 3

Abstract

Our purpose is to seek that the reachable set of the semilinear system $\frac{d}{dt}x(t){\;}={\;}Ax(t){\;}+{\;}f(t,x(t)){\;}+{\;}Bu(t)$ 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

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