Robust stabilization of stochastic Markovian jumping systems via proportional-integral control

This paper studied the proportional-integral (PI) control problems of stochastic Markovian jump systems (MJSs) with uncertain parameters. Under complete access to the system states, the PI controller design procedure turns to static output feedback control problem that make the closed-loop dynamics of this class of uncertain MJSs be robustly stochastically stable. A sufficient condition on the existence of PI controller is presented and proved by means of linear matrix inequality techniques. The presented results are extended to the case when the system states are not accessible. In order to make the relative equations approximate with a satisfactory precision, we described the problem as a semidefinite programming one via disciplined convex optimization. Simulation results illustrate the validity of the proposed algorithms.

► The PI controller through time-domain approach of MIMO Markovian jumping systems has been firstly investigated.
► And an effective robust PI controller was designed to stabilize the control dynamics.
► The presented results are also feasible to the case when the system states are not accessible.
► To make the relative equations approximate with a satisfactory precision, the problem was described as a semidefinite optimization one via disciplined convex programming.