The time-sharing hierarchical control of discrete-time large-scale systems: fixed switching case

This paper deals with new control strategies problem for discrete-time large-scale systems. Most academic control schemes for large-scale systems are decentralized control, which assume all the control variables are updated simultaneously. But decentralized control of large-scale systems has much inadequacy when the dimension of the systems is sufficient large. A new large-scale system control strategy-- time-sharing control strategy is considered by thinking of time-sharing communications, it takes the strategy: control input to take the initiative each time only for a sub-system, the control input of other subsystems remain unchanged, although the control strategy adopted is to centralized control strategy, but actually it is a decentralized control effect. By means of the linear matrix inequality (LMI) approach, sufficient conditions for existence of time-sharing hierarchical controllers of discrete-time large-scale systems for fixed switched case is given in terms of linear matrix inequalities (LMIs), respectively. When these LMIs are feasible, explicit expressions of time-sharing controller is obtained. An illustrative example is given to demonstrate the validity and applicability of the proposed approach.