A class of $L_1$-to-$L_1$ and $L_\infty$-to-$L_\infty$ interval observers for (delayed) Markov jump linear systems

TL;DR

This paper develops efficient linear programming-based interval observers for positive Markov jump linear systems, including systems with delays, providing necessary and sufficient conditions for $L_1$ performance and sufficient conditions for $L_$ performance.

Contribution

It introduces a novel class of interval observers for MJLS with explicit conditions formulated as linear programs, applicable to systems with and without delays.

Findings

Conditions for $L_1$ performance are necessary and sufficient.

Conditions for $L_$ performance are sufficient.

Two illustrative examples demonstrate the approach.

Abstract

We exploit recent results on the stability and performance analysis of positive Markov jump linear systems (MJLS) for the design of interval observers for MJLS with and without delays. While the conditions for the $L_1$ performance are necessary and sufficient, those for the $L_\infty$ performance are only sufficient. All the conditions are stated as linear programs that can be solved very efficiently. Two examples are given for illustration.