H∞ control for Poisson-driven stochastic systems

Highlights：

• The martingale theory is utilized to deal with the jump item and the sum of stochastic integrals with respect to the continuous part of states in Itô formula, and then we gives an equivalent Itô formula for stochastic differential equations driven by compensated Poisson process.

• Based on these, this paper designs an H∞ controller by means of a linear matrix inequality, which is fairly straightforward to be solved.

• The designed result contains information about the average number of jump random events in a unit time, and one can use convex optimization algorithm easily to estimate the maximum average number of jump random events in a unit time that the system can undergo to achieve the stability and control performance.

摘要

•This paper uses the Doob-Meyer decomposition and measure theory to give a model transfor-mation method, and Poisson-driven stochastic systems are transformed into stochastic systems driven by compensated Poisson process. Since compensated Poisson process is a martingale, we can use effective properties and tools in martingale theory to investigate the H∞ control problem.•The martingale theory is utilized to deal with the jump item and the sum of stochastic integrals with respect to the continuous part of states in Itô formula, and then we gives an equivalent Itô formula for stochastic differential equations driven by compensated Poisson process.•Based on these, this paper designs an H∞ controller by means of a linear matrix inequality, which is fairly straightforward to be solved.•The designed result contains information about the average number of jump random events in a unit time, and one can use convex optimization algorithm easily to estimate the maximum average number of jump random events in a unit time that the system can undergo to achieve the stability and control performance.