Physics

Mathematics

Mathematical analysis

Artificial intelligence

Control (management)

Frequency domain

Computer science

Jump

Quantum mechanics

Applied mathematics

Control theory (sociology)

IEEE Transactions on Systems Man and Cybernetics Systems

Incorporating the disturbance frequency into system analysis and synthesis, this paper is dedicated to the quantized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H_\infty }$ </tex-math></inline-formula> 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.

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