Mean square stabilizability of continuous-time linear systems with partial information on the Markovian jump parameters

We provide necessary and sufficient conditions for mean square (MS) stabilizability of continuous-time linear systems with Markovian jumps in the parameters subject to the partial information on this jump variable. We assume that the Markovian jump parameter is not exactly known, but instead an estimate of it is available to the controller. Under some additional assumptions, a solution via linear matrix inequality is also provided. The results apply, in a unified basis, to the homogeneous case and two scenarios regarding additive disturbances: the one in which the system is driven by a Wiener process, and the one characterized by functions in L₂^m(R⁺), which is the usual scenario for the H_∞ approach. It is also shown that MS stabilizability is equivalent to L₂ⁿ stabilizability whenever the disturbances are in L₂ ^m(R⁺)