Robust stabilization and guaranteed cost control of large scale linear systems with jumps

In this paper we consider systems which are linear in the continuous plant state and whose mode dynamics is described via random jumps modelled by a discrete-state Markov chain. By the use of decomposition and coordination leading to a two level control system, the robustness in the sense of robust stability and guaranteed cost control is ensured for the partly unknown large scale linear system with markovian jumps. Decision makers on each level have different models of the system and instantaneous information. Two different structures are proposed: decentralized and centralized one. In the decentralized structure control strategy combines the linear control law resulting from a solution of the JLQ problem for local decision makers and the nonlinear one of the coordinator who takes into account bounds imposed on the uncertainty disturbing the overall system and interconnections between subsystems. In the centralized structure decision maker of the upper level has only nominal linear model of the system neglecting uncertainties. A centralized controller is found using the quadratic criterion for the system and incorporates the information about its state. The role of the local decision maker is to ensure robust stability and guaranteed cost in spite of uncertainties represented by deviation of parameters and disturbances.