A Quadratic Approach to Rejection of Amplitude-Bounded Input Disturbances

This paper provides a quadratic approach to rejection of amplitude-bounded input disturbances for single-input linear discrete-time systems. Control specification is that a quadratic form decreases along the state trajectories when a quadratic constraint on the state is violated. All the state-feedback controllers that satisfy the specification are parameterized using the solution of the Riccati equation in cheap optimal control. The robustness of the controllers represented by the maximum allowable amplitude of disturbances is not uniform over the state space and proportional to the constrained value. In special cases, the optimal performance is represented using system parameters such as unstable zeros of the plant.