A New Approach to the Energy-to-Peak Performance Analysis of Continuous-Time Markov Jump Linear Systems

The energy-to-peak (L2–L∞) performance of continuous-time Markov jump linear systems (MJLS) is studied from a new perspective: by considering an output norm which is different from the one treated in the existing MJLS literature, we devise upper and lower bounds to the worst-case energy-to-peak gain (L2–L∞ induced norm). The lower bound can be efficiently computed by solving an ordinary differential equation, or, if the jump process is irreducible, a Lyapunov (algebraic) equation. The upper bound is obtained from the controllability Gramian of the MJLS (a set of coupled Lyapunov equations). As a by-product of this result, we are also able to show the consistence of the corresponding L2–L∞ system norm vis-à-vis the H2 norm of MJLS: it is proven that the H2 norm is an upper bound to the worst-case energy-to-peak gain, a feature which was not proven in other works devoted to the MJLS case. In the case without jumps, it is shown that both bounds coincide with the actual L2–L∞ system norm.