Controllability, stability and pole allocation for jump linear systems

One studies the properties of controllability and stabilisability for a class of linear systems with stochastic jumps in parameter values. Stability is analysed by Liapounov direct method, and the Liapounov exponent of the solution is exactly computed. A pole allocation result is also obtained: provided the system satisfies a certain algebraic controllability test, it is possible tc arbitrarily assign the poles of the averaged dynamic matrix.