  This paper discusses the stability analysis of linear parameter varying
systems with a parameter-dependent delay where the parameters are assumed to be
stochastic piecewise constants under spontaneous Poissonian jumps. Based on
stochastic Lyapunov-Krasovskii functionals, we also provide sufficient
synthesis conditions for the gain-scheduled state-feedback controller with
memory in terms of parameter-dependent linear matrix inequalities (LMIs). Such
synthesis conditions are computationally intractable due to the presence of
integral terms. However, we show that these LMIs can be equivalently
represented by integral-free LMIs, which are computationally tractable.
Finally, we illustrate the applicability of the results through examples.
