Mean Square Stabilizability of Continuous-Time Linear Systems with Partial Information on the Markovian Jumping Parameters

Abstract

We provide necessary and sufficient conditions for mean square (MS) stabilizability of continuous-time linear systems with Markovian jumps in the parameters LSMJP subject to 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 LMI (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 (ℝ⁺), which is the usual scenario for the H _∞ approach. It is also shown that MS stabilizability is equivalent to -stabilizability whenever the disturbances are in (ℝ⁺).

Key Words:

• Mean square stabilizability
• Jump parameter
• Continuous-time linear systems
• Partial information

AMS (MOS) Subject Classification:

• 90D

Acknowledgment

Research supported in part by the Brazilian National Research Council-CNPq, under the Grant No. 520169/97.2 and Grant No. 305173/88-0, by the Research Council of the State of São Paulo-FAPESP, Grant No. 97//04668-1, by PRONEX/CNPq Grant No. 66.2015/98-3, and by IM-AGIMB.