A Class of ${L}_{1}$ -to- ${L}_{1}$ and ${L}_{\infty}$ -to- ${L}_{\infty}$ Interval Observers for (Delayed) Markov Jump Linear Systems

We exploit recent results on the stability and performance analysis of positive Markov jump linear systems for the design of interval observers for Markov jump linear systems with and without delays. While the conditions for the ${L} _{\textbf {1}}$ performance are necessary and sufficient, those for the ${L} _{\boldsymbol {\infty }}$ performance are only sufficient. All the obtained conditions are stated as linear programs, well-known for their tractability and scalability. Two examples are given for illustration.