H∞ filtering of continuous Markov jump linear system with partly known Markov modes and transition probabilities

TLDR: A stochastic variable satisfying the Bernoulli random binary distribution is employed to describe the accessibility of Markov mode to the designed filter assuring stochastically stability and a prescribed H ∞ performance level for the resulting filtering error system.

Abstract: This paper studies the H ∞ filtering problem for continuous Markov jump linear systems (MJLSs) with partly accessible Markov modes and transition probabilities. A stochastic variable satisfying the Bernoulli random binary distribution is employed to describe the accessibility of Markov mode to the designed filter. Meanwhile, the transition probabilities are allowed to be known, unknown with known lower and upper bounds and completely unknown. Attention is focused on designing a partially mode-dependent H ∞ filter assuring stochastic stability and a prescribed H ∞ performance level for the resulting filtering error system. With resorting to a matrix transformation technique to separate Lyapunov variables from system matrices, sufficient conditions are established in terms of linear matrix inequalities (LMIs). It is worth mentioning that the proposed method covers the existing results as special cases. Finally, a numerical example is given to show the effectiveness of the proposed method.