The authors study the generalized discrete self-trapping system formulated in terms of the \(\text{u}(n)\) Lie-Poisson algebra as well as as its noncompact analog given on the \(\text{gl}(n)\) algebra. The Hamiltonian is a quadratic-linear function of the algebra generators where the quadratic part consists of the squared generators of the Cartan subalgebra only: \[ H = \sum^ n_{i = 1}(\gamma_ i/2)A^ 2_{ii} + \sum^ n_{i,j} m_{ij}A_{ij}. \] Two integrable cases are discovered: one for the \(\text{u}(n)\) case and the other for the \(\text{gl}(n)\) case. The corresponding \(L\)-operators (\(2\times 2\) and \(n \times n\)) are found which give the Lax representation for these systems. The integrable model on the \(\text{gl}(n)\) algebra looks like Toda lattice because in this case \(m_{ij} = c_ i\delta_{ij - 1}\). The corresponding \(2\times 2\) \(L\)-operator satisfies the Sklyanin algebra.