Delay-dependent robust stability and H∞H∞ control for jump linear systems with delays

This paper considers robust stochastic stability, stabilization and H∞H∞ control problems for a class of jump linear systems with time delays. By using some zero equations, neither model transformation nor bounding for cross terms is required to obtain the delay-dependent results, which are given in terms of linear matrix inequalities (LMIs). Maximum sizes of time delays are also studied for system stability. Furthermore, solvability conditions and corresponding H∞H∞ control laws are given which provide robust stabilization with a prescribed H∞H∞ disturbance attenuation level. Numerical examples show that the proposed methods are much less conservative than existing results.