Output-feedback stabilization control of linear systems with random switchings and state jumps

We are concerned with the stabilization control problem for a class of systems with random switchings and state jumps. We suppose the random switching signal to obey Poisson distribution and intend to use output-feedback control to achieve stabilization. Firstly, based on the statistic property of the distribution of switching points, we derive some sufficient conditions to guarantee the closed-loop system to be almost surely exponentially stable. Then, we pose a parametrization approach to convert the construction conditions of the output-feedback control into a family of matrix inequalities.