Stable controlling analysis for discrete singular bilinear systems

The stability problem for a discrete singular bilinear system is investigated.The existing conditions of stable controlling for discrete singular bilinear systems are studied and the corresponding controlling scheme is given.By decomposing the singular system and applying Lyapunov method,it is proved that linear state control can make a closed loop system asymptotically stable around the origin.By constructing singular Lyapunov function,the conditions of making a closed loop system stable under the condition not decomposing the system are also researched.The proof of the relevant theory for the discrete singular bilinear system may be regarded as the extension of the normal discrete bilinear system.