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Almost sure stability and transient behavior of stochastic nonlinear jump systems motivated by networked control systems

The stability of networked control systems (NCS) can be analyzed using jump systems where the jumping characterizes packet loss or delay. This motivates our investigations on nonlinear jump systems (NLJS). In many cases, the transient behavior of such a system, i.e. the convergence rate to the equilibrium, is much more interesting than the mere stability. In this paper, we extend a recent result that describes this transient behavior for NCS with packet loss to NCS with random delays. In other words, the jump system exhibits an arbitrary but finite number of discrete states instead of only two states. In addition, we considerably reduce the conservatism of the former result, which is shown theoretically and through a simple numerical example.