On the Stability Properties of Spline Approximations for Retarded Systems

F. Kappel, D. Salamon
1989 SIAM Journal of Control and Optimization  
This paper studies the qualitative properties of the spline approximation scheme for retarded functional differential equations introduced by Kappel and Salamon [SIAM J. Control Optim., 25 (1987), pp. 1082-1117. It is shown that the approximating systems are stable for large N if the underlying retarded functional differential equation is stable. In this case the approximating equations are in some sense uniformly (with respect to the approximation index) stable in the vector component of the
more » ... component of the state but not so in the complete state.
doi:10.1137/0327021 fatcat:kgtn5zd5ufg47aoq73quhwuwei