The Markov model of a dynamic system based on experimental data for control problems of bionic prostheses

The paper states that the Markov transition update is Pt+Δt = M Pt with entries Mi,j formed from empirical transition frequencies, asserts by Perron–Frobenius that the spectral radius is one, and introduces modal formulas f = arg(λ)/(2πΔt) and ξ = ln|λ|/(2π f Δt) for complex modes; it also proposes the hypercubic neighbor rule yielding N ≈ n/2 in N dimensions. All of these appear explicitly in the PDF, including the Perron claim and the frequency/decrement definitions, and the n ≈ 2N neighbor-count heuristic for a continuous signal . However, the paper incorrectly writes a generic “diagonalization” as M = Φ λ Φ^T (orthogonal diagonalization), which is false for non-symmetric Markov matrices; the correct form is M = V Λ V^{-1}, and additional conditions (irreducibility, aperiodicity) are needed for uniqueness/simplicity of the Perron root. Normalization (row vs column stochastic) is not made explicit. The model solution fixes these points: it uses the correct V Λ V^{-1} decomposition, states the stochastic normalization and 1-norm bound for ρ(M), and supplies mild geometric hypotheses under which the neighbor-count estimator N̂ = n/2 is consistent. Thus, the model is correct and more rigorous, while the paper is incomplete and contains a key linear-algebra misstatement .