Approximate controllability of discrete semilinear systems and applications
Approximate controllability of discrete semilinear systems and applications
In this paper we study the approximate controllabilityof the following semilinear difference equation\[z(n+1)=A(n)z(n)+B(n)u(n)+f(n,z(n),u(n)), \quad n\in \mathbb{N}^*,\]$z(n)\in Z$, $u(n)\in U$, where $Z$, $U$ are Hilbert spaces, $A\inl^{\infty}(\mathbb{N},L(Z))$, $B\in l^{\infty}(\mathbb{N},L(U,Z))$, $u\inl^2(\mathbb{N},U)$ and the nonlinear term $f:\mathbb{N} \times Z\timesU\longrightarrow Z$ is a suitable function. We prove that, undersome conditions on the nonlinear term …