Robust decentralized control of stochastic systems with jumps

A class of complex control systems, modelled as a finite family of stochastic differential equations with state-dependent noise is considered. Each individual equation of this family describes the plant state variable in individual regime of the system composed of a set of interconnected subsystems. The transitions between these regimes are discontinuous and are modelled by a homogeneous Markov chain. At the moment of regime change (jump of Markov chain) the plant state can change by jump too. The robust decentralized control in the form of a set of switching local feedbacks which guarantees exponential stability in the mean square (ESMS) of closed loop system for given noise intensities and for all transition probabilities of the Markov chain from the given domain is obtained. The perfect robust control in the same decentralized form which guarantees ESMS of closed loop system independently of the transition probabilities is also obtained. In partial case, when the plant state variable is changed without jumps, the perfect robust control is obtained in more simple non-switching form.