H∞ control of discrete-time systems with norm-bounded uncertainties and time delay in state

Studies the problem of H_∞ control for discrete-time systems with norm-bounded uncertainties and time delay in state. The sufficient conditions for the existence of H_∞ filters are derived in terms of a special kind of nonlinear matrix inequality P>g(P), which can be solved by a simple recursive algorithm. Moreover the design method of H_∞ control is obtained. The advantage of this approach is that there may be the chance to select the gain K=h(P), where h(.) is a matrix function. The results of Song Seong-Ho and Kim Jeom-Keun (1998) is a special case of the main results in this paper. A numerical example is given to illustrate the main results