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This work deals with a sliding mode control scheme for discrete time nonlinear systems. The control law synthesis problem is subdivided into a finite number of subproblems of lower complexity, which can be solved independently. The sliding mode controller is designed to force the system to track a desired reference and to eliminate unwanted disturbances, compensating at the same time matched and unmatched parameter variations. Then, an observer is designed to eliminate the need of the state in the controller implementation. This design technique is illustrated determining a dynamic discrete time controller for induction motors.

In this work a class of nonlinear controllers has been derived for spacecraft with flexible appendages. The control aim is to track a given desired attitude. First, a static controller based on the measure of the whole state is determined. Then, a dynamic controller is designed; this controller does not use measures from the modal variables, and the variables measured are the parameters describing the attitude and the spacecraft angular velocity. Finally, it is shown that a relaxed version of the tracking problem can be solved when the only measured variable is the spacecraft angular velocity. Simulations show the performances of such control schemes.

Robust feedback control of a synchronous motor with model and parameter uncertainties and load disturbances is studied. The mathematical description of the motor in the (d, q) frame yields a bilinear model in state space form. The control strategy is based on a worst-case analysis and leads to the formulation of a min–max problem, whose solution provides an H∞ bound for the noise-to-output transfer function. The design of the dynamic controller entails the solution of an appropriate Riccati equation.