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The problem of analysis and parameter estimation by means of the Taylor operational matrix is addressed. The goals are twofold. For system analysis, variables of the deterministic bilinear system with time-varying parameters are expanded into Taylor polynomials, and the solution of a differential equation is reduced to that of a linear algebraic matrix equation. The second goal is to estimate the unknown parameters of time-invariant deterministic bilinear systems. Numerical examples with satisfactory results are given to show the usefulness of this approach.