Reduced Order H∞ Observer Design for One-Sided Lipschitz Nonlinear Continuous-Time Singular Markov Jump Systems

The reduced order H-infinity observer design problem for one-sided Lipschitz nonlinear continuous-time singular Markov jump systems is discussed in this paper. With the assumptions that the nonlinear term satisfies the one-sided Lipschitz condition and the quadratic inner-bounded condition, a sufficient condition is given to guarantee both the stochastic stability and a prescribed H-infinity performance of the error dynamics. By using a matrix generalized inverse technique, the sufficient condition is transformed into a linear matrix inequalities (LMIs) format. Ultimately, a numerical example is provided to demonstrate the applicability of the proposed design.