$\mathcal H_{2}$ Performance Analysis and Applications of 2-D Hidden Bernoulli Jump System

Abstract

The asymptotic mean square stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> 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 H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> 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.