On Quantization in Discrete-Time Control Systems: Stability Analysis of Ternary Controllers

This paper studies feedback system with a state-feedback law with a ternary nonlinearity in the feedback loop. We propose a novel Lyapunov-based approach that takes advantage of a framework recently developed to assess positivity of generalized piece-wise quadratic forms. Such an approach is used to compute piece-wise quadratic function as stability certificates of the non-linear system.