Title :
A remark on the converging-input converging-state property
Author :
Sontag, Eduardo D.
Author_Institution :
Dept. of Math., Rutgers Univ., Brunswick, NJ, USA
Abstract :
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.
Keywords :
asymptotic stability; convergence; multidimensional systems; asymptotic stability; asymptotically stable equilibrium; bounded trajectory; converging-input converging-state property; domain of attraction; finite-dimensional controlled systems; unforced system; Asymptotic stability; Chemicals; Control systems; Extraterrestrial measurements; H infinity control; Instruction sets; Jacobian matrices; Mathematics; Steady-state;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2002.808490
