Controlling coexisting attractors of a class of non-autonomous dynamical systems

Both the paper and the candidate solution hinge on the same core Lyapunov-step expansion and the per-step inequality (8), and both appeal to the aggregated condition (9) to conclude V(τ*) = O(h^2). However, neither establishes that (9) actually follows from Algorithm 1 under the stated bounds, nor do they give feasibility/non-emptiness conditions for Step 1’s “feasible range.” The paper’s derivation of the one-step formula (14) explicitly uses a linearly time-varying control within each step, while Algorithm 1 is described as zero-order hold; this implementation/analysis mismatch is not resolved in the paper. The model’s solution smooths this by adopting a ramp control, but it likewise assumes (9) and does not prove feasibility under M1, M2. Hence, both arguments are essentially the same and incomplete on the key existence/feasibility step and on deriving (9) from the algorithm rather than assuming it. See Algorithm 1 and Theorem 2.1 with (8)–(9) , the distance definition and control law (6)–(7) , the one-step second-order expansion (14) with O(h^3) remainder , and the concluding bound “hence ⟨d(τn*), d(τn*)⟩ ≤ c1 h^2” . The definition of controllability used by the paper is explicit (Definition 2.1) .