On the adaptive stabilization of linear stochastic systems with jump process parameters

Consideration is given to the situation in which a completely observed stochastic process is generated by a linear stochastic system whose unobserved parameters constitute a Markov process evolving on a finite set Θ of linear systems. Subject to a new controllability condition applying to the set Θ, it is shown that an adaptive control law, generated by the use of the Wonham nonlinear filter for the parameter values and a heriditary Riccati equation for the feedback gain, stabilizes the system in both the mean square and sample average sense