On uniform convergence in Markov jump linear systems problems and the Kolmogorov forward equation

Uniform convergence of standard transition matrices is a concept which appears in some fundamental results in Markov chain theory and therefore in optimal control, H/sub /spl infin// control and stability problems of continuous time Markov jump linear systems (MJLS) with infinite countable state space of the Markov chain. We identify some classes of standard transition matrices P = (p/sub ij/(t))/sub i,j//spl isin/N that exhibits j-uniform convergence of (o/sub ij/(t))/t = (p/sub ij/(t)-p/sub ij/(0)-p/spl dot//sub ij/(0)t)/t as t /spl rarr/ 0, using tools such as analysis of j-uniform convergence and a version in l/sub 1/ of the forward equation.