Quantized $H_\infty$ Output Control of Linear Markov Jump Systems in Finite Frequency Domain

Incorporating the disturbance frequency into system analysis and synthesis, this paper is dedicated to the quantized ${H_\infty }$ static output control of linear Markov jump systems. The output quantization is transformed into a sector bound form, and the finite frequency performance is handled by Parseval’s theorem. With the aid of Finsler’s lemma, sufficient conditions for the resulting closed-loop system are first established to satisfy the required finite frequency performance. To treat the static output feedback control problem in the framework of linear matrix inequalities, a new strategy is developed to decompose the coupling among Lyapunov variables, controller gain, and system matrices. In contrast to the existing results in the literature, no additional assumptions are imposed on the system matrices. Numerical examples are presented to demonstrate the validity of the established results.