Discrete-Time Robust Steady-State Control of Nonlinear Multivariable Systems: A Unified Approach

The steady-state control of multivariable nonlinear discrete-time, time-invariant systems in the presence of arbitrary unmeasurable but bounded disturbances is addressed in this paper. The pseudoinverse model approach as a unified concept to cope with possible noninvertibility and to achieve a desired behavior of a wide class of both linear and of nonlinear multi-input multi-output square and also nonsquare systems is proposed. It is assumed that the number of the system outputs is not less than the number of its control inputs. Some results regarding equilibrium states are given. In particular, it is shown that the equilibrium state may not exist, in general. A simple linear pseudoinverse-based controller of the integral action is designed for regulating these nonlinear multivariable systems. The properties of robust stability and the boundedness of all signals caused by this controller are derived. Numerical examples are given to support the theoretical investigations.