Design issues in stochastic adaptive control of discrete-time systems using multiple models

Several design issues in the stochastic adaptive control of discrete-time systems using multiple models are discussed in this paper. First, a memory factor is introduced in order to deal with time-varying environment. Next, the disturbance rejection problem is solved by proper parameterization of the multiple models. Following this, the relaxation of the strict positive realness condition is discussed. Finally, extensions to MIMO systems for both deterministic and stochastic cases is presented. By utilizing the interactor matrix, it is shown that all the stability analysis for the SISO systems can naturally be extended to MIMO systems.