Disturbance attenuation for Markov jump linear system over an additive white Gaussian noise channel

ABSTRACT

This paper studies the stabilisability and the performance of stochastic disturbance attenuation of a Markov jump linear system whose feedback channel is subject to an additive white Gaussian noise. First an inequality of differential entropy of random vectors under Markov switching is presented. Then by the concept of entropy power and the theory of information, a necessary condition to stabilise the system is obtained. This requires that the signal-to-noise ratio in the feedback channel is bigger than a specified value. Furthermore, to evaluate the performance of disturbance attenuation, a lower bound of the maximum fluctuation of the system state is presented.

KEYWORDS:

• Disturbance attenuation
• Markov jump linear systems
• differential entropy
• signal-to-noise ratio

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Funds of China [61573237, 61533010]; Shanghai Natural Science Fund [13ZR1416300]; Open Project of Key Laboratory of Advanced Process Control for Light Industry [APCLI1204]