Necessary and Sufficient Conditions for Adaptive Stabilizability of Continuous-Time Markov Jump Linear Stochastic Systems
The purpose of this paper is to provide a mathematically rigorous solution to a well-known problem in stochastic adaptive control, i.e., to find the weakest possible structural condition for global stabilizability of continuous-time Markov jump linear stochastic systems with known candidate modes but with an unobservable Markov parameter process. Under some regularity assumptions, it is shown that the necessary and sufficient condition for global adaptive stabilizability hinges on the solvability of the same coupled Riccati equations as in the non-adaptive case. This result highlights a fundamental difference between the continuous-time case considered here and the discrete-time case studied earlier by Xue and Guo (2001), in which the coupled Riccati equations for adaptive and non-adaptive stabilizability are different.