Stabilization of a nonlinear multivariable discrete-time time-invariant plant with uncertainty on a linear pseudoinverse model

This paper addresses the problem of the robust stabilization of a nonlinear multivariable time-invariant plant on a semi-infinite discrete time interval under arbitrary nonmeasurable bounded additive disturbances. A guaranteed value of the quality criterion is given by the functional representing the weighted sum of the limiting norms of the control vectors and output variables. To generate control actions, a controller containing a linear generalized inverse model and discrete-time integrators is introduced into the feedback loop. Sufficient conditions for the robust stability of the control system, as well as the conditions for the ultimate boundedness of all its signals (dissipativity conditions), are formulated. A corresponding simulation example is presented.