This letter addresses the <tex-math notation="LaTeX">H₂ </tex-math> output-feedback control problem for continuous-time semi-Markov jump linear systems (S-MJLS) with Erlang dwell times. To this end, we exploit the fact that any Erlang-distributed variable may be expressed as the sum of exponential random variables to devise a Markov-jump system equivalent to the original S-MJLS. This equivalence allows us to derive finite-dimensional control design conditions for Erlang S-MJLS. Numerical examples illustrate the main features of the results presented in the letter.
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Souza et al. (2022) studied this question.
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