Stability analysis of weighted multiple model adaptive control of a linear time-invariant discrete-time system

The paper is concerned with the long-standing problem of the stability of weighted multiple model adaptive control (MMAC). Based on virtual equivalent system (VES) concept and methodology, a positive answer to the problem is presented under a unified framework which is independent of specific `local´ control strategy and specific algorithm for weight calculation. The obtained results indicate that the stability of a weighted MMAC system depends mainly on the convergence of posterior probability weights, i.e., the posterior probability corresponding to the model closest to the true plant converges to 1, and others converge to 0.