A remark on the converging-input converging-state property

A remark on the converging-input converging-state property

Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This “well-known” but hard-to-cite fact is proved and slightly generalized here.

M ay 2 00 2 a remark on the converging - input converging - state property Eduardo

Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This “well-known” but hard-to-cite fact is proved and slightly generalized here.

Remarks on the Lp-input converging-state property

Consider a system ẋ = f(x) + g(x)u (f and g locally Lipschitz) with the property that the associated autonomous system ż = f(z) has an asymptotically stable compactum C with region of attraction A. Assume that x is a solution of the former, defined on [0,∞), corresponding to an input function u. A simple proof is given of the following L -input converging-state property: if u ∈ L for some p ∈ [...

NBIC, THE CONVERGING TECHNOLOGIES

On the Uniquely Converging Property of Nonlinear Term Rewriting Systems

A uniquely converging (UC) property for a possibly nonlinear term rewriting system (TRS) is investigated. UC, which is an intermediate property between conventional Church-Rosser (CR) and uniquely normalizing (UN), is newly proposed in connection with the consistency of continuous semantics. Continuous semantics is de ned by constructing free-continuous algebra which is required in algebraic sp...