Nonfragile mixed $$\varvec{H}_{\varvec{\infty }}/\varvec{l}_{\varvec{2}} -\varvec{l}_{\varvec{\infty }}$$ state estimation for repeated scalar nonlinear systems with Markov jumping parameters and redundant channels.

This paper gives attention to the issue of nonfragile state estimation for a class of Markov jump systems with repeated scalar nonlinearities and redundant channels. A mixed $$\mathcal {H}_{\infty }$$ and $$ l_{2}-l_{\infty }$$ performance index is introduced to optimize the state estimation performance. Assisted by the introduced random variables, this paper constructs a new type of communication models to give a description of multi-channel packet dropout. With the aid of the Lyapunov-Krasovskii function, a sufficient condition is derived, which assures the error dynamic is stochastically stable conforming with the prespecified mixed $$\mathcal {H} _{\infty }$$ and $$l_{2}-l_{\infty }$$ performance. Eventually, a numerical example is proposed to exactly reflect the applicability of this creative method. [ABSTRACT FROM AUTHOR]