Disturbance-observer-based-L<inf>2</inf> — L<inf>∞</inf>-control for Markovian jump nonlinear systems with general uncertain transition rate

Abstract

In this paper, the problem of disturbance-observer-based-L 2 – L ∞ -control (DOBC) is discussed for Markovian jump nonlinear systems with general uncertain transition rate and multiple disturbances. The general uncertain transition rate matrix means that some elements of the transition rate matrix are only known their bounds, and the others are unknown. The disturbances can be divided into two parts: one is described by an exogenous system in the input channel, and the other is supposed to be H 2 norm bounded. A disturbance observer is designed to estimate the disturbances which are described by an exogenous system, and the estimation is applied to feedforward compensation. Sufficient conditions are derived in terms of linear matrix inequalities under the closed-loop system stochastic stability with L 2 – L ∞ performance can be guaranteed. Finally, an application example is given to illustrate the effectiveness of proposed approach.