Fault-tolerant design of decentralized H/sub /spl infin// control systems using homotopy method

This paper considers a fault-tolerant decentralized H/sub /spl infin// control problem for multi-channel linear time-invariant systems. The aim is to design a decentralized H/sub /spl infin// output feedback controller to make the given system stable and achieve a certain H/sub /spl infin// performance both in the normal situation and in the situation where any one of the local controllers fails. The control problem is reduced to a feasibility problem of a set of bilinear matrix inequalities (BMIs). An algorithm is proposed to solve the BMIs. First, the normal situation is considered where all the local controllers are functioning. The local controllers are obtained by using a homotopy method from a standard centralized H/sub /spl infin// controller imposing a structural constraint gradually. Second, the above case is extended to the one where any one of the local controllers fails. We again use a homotopy method where the coefficients matrices of the failure controller are decreased gradually to zero. The efficiency of the proposed algorithm is demonstrated by an example.