$mathcal H_{2}$ Performance Analysis and Applications of 2-D Hidden Bernoulli Jump System Academic Article uri icon

abstract

  • IEEE The asymptotic mean square stability and H₂ performance of the 2-D hidden Bernoulli jump system is analyzed in this paper. This system, essentially, has a bi-jumping property, in other words, its jumps depend on two jumping parameters, one is the Bernoulli process, the other is dependent on the Bernoulli process via a conditional probability matrix, they together determine which subsystem is active and are coined as hidden Bernoulli model. By means of Lyapunov function method, a sufficient condition is derived, which reveals that the system is asymptotically mean square stable and has a certain H₂ performance if a set of matrix inequalities are satisfied. Furthermore, the issues of asynchronous control and filtering are addressed for 2-D Bernoulli jump system based on the hidden Bernoulli model and the derived result. Finally, numerical simulations indicate that these proposed theories and methods are reliable and efficient.

author list (cited authors)

  • Wu, Z., Shen, Y., Su, H., Lu, R., & Huang, T.

citation count

  • 14

publication date

  • September 2017