A class of $L_1$-to-$L_1$ and $L_\infty$-to-$L_\infty$ interval observers for (delayed) Markov jump linear systems
It provides a new design method for interval observers in a class of stochastic hybrid systems, but the results are incremental as they extend existing positive system techniques to Markov jump systems.
The paper designs interval observers for Markov jump linear systems with and without delays using positive system theory, providing necessary and sufficient conditions for L1 performance and sufficient conditions for L∞ performance, formulated as linear programs.
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.