Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

Abstract

This study addresses the stabilization condition for Markovian jump systems with quantized input and generally uncertain transition rates. To stabilize Markovian jump systems with nonlinear inputs using only partial knowledge regarding to the transition rates, the proposed controller is designed as two control parts: a linear control part for stabilizing the system and a nonlinear control part for eliminating undesirable effects from the quantized input. Moreover, an appropriate weighting method, using lower and upper bounds of the partial transition rate, is employed to derive a less conservative stability condition. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed controller.

The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates

“…Then, using the Schur complement, it can be shown that ( 43) implies (27). Furthermore, from Condition (30), the LMI condition in ( 23) can be obtained by…”

“…The method reported in Ref. [28] has piqued the interest of researchers [29,30] concerning the stabilization problem of MJSs. These results all focus on the uncertainties of the transition rates, but there is no consideration of external disturbances.…”