Stabilization of continuous-time jump linear systems

We investigate almost-sure and moment stabilization of continuous time jump linear systems with a finite-state Markov jump form process. We first clarify the concepts of δ-moment stabilizability, exponential δ-moment stabilizability, and stochastic δ-moment stabilizability. We then present results on the relationships among these concepts. Coupled Riccati equations that provide necessary and sufficient conditions for mean-square stabilization are given in detail, and an algorithm for solving the coupled Riccati equations is proposed. Moreover, we show that individual mode controllability implies almost-sure stabilizability, which is not true for other types of stabilizability. Finally, we present some testable sufficient conditions for δ-moment stabilizability and almost-sure stabilizability.