Stochastic stability of nonlinear sampled data systems with a jump linear controller

This paper analyzes the stability of a sampled-data system consisting of a deterministic, nonlinear, time-invariant, continuous-time plant and a stochastic, discrete-time, jump linear controller. The jump linear controller models, for example, computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled-data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.