Robustness Margins for Continuous-time Markov Jump Linear Systems with Uncertain Transition Rates

Abstract

In this paper we introduce new robustness margins for continuous-time Markov jump linear systems (MJLS) with uncertain transition rates. Our approach is able to ensure robustness with respect to transition rate uncertainties that satisfy a spectral norm bound, a setup where no previous studies seem to exist in the literature. As shown in the paper, this paradigm is amenable to a linear time-invariant description, and therefore classical disturbance attenuation techniques can be employed. The robustness margins that constitute our main results (based on mean square stability and mean stability notions) are characterized by LMIs (linear matrix inequalities). They include both analysis and synthesis methods that, when compared to other results from the literature, have the favorable feature of being amenable to convex optimization (in the sense that they can be efficiently maximized in computer implementations). Two numerical examples show how our approach can outperform some existing results from the literature.