A Parametrization of Controllers Quadratically Stabilizing Single-Input Discrete-Time Systems under Bounded Disturbances⁎. Issue 25 (2018) - Shingin, Hidenori
Abstract: This paper presents a parametrization of static state-feedback controllers that stabilize a discrete-time linear system with single control input corrupted by disturbances with bounded amplitude. All stabilizing controllers that suppress a quadratic form of the state are parametrized by a positive definite matrix corresponding to the weight on the state in cheap control. Asymptotic stability is also guaranteed by such controllers except for some extreme cases. This parametrization enables to evaluate the decrement of a quadratic Lyapunov function and the magnitude of control values.