Finite-Horizon ${l}_{2}-{l}_{\infty}$ State Estimation for Networked Systems Under Mixed Protocols

Abstract

Dear Editor, This letter is concerned with the finite-horizon <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{2}-l_{\infty}$</tex> state estimation (SE) problem for a class of networked time-delay systems where the measurements are transmitted through two individual communication channels. With the aim of preventing the transmitted data from conflicts, the signal transmissions over such the communication channels are scheduled by different communication protocols, namely the stochastic communication protocol (SCP) and Round-Robin protocol (RRP). A mixed scheduling model is proposed to describe the transmission behaviors subject to such two protocols. The objective of this letter is to design an estimator such that the estimation error achieves the desired finite-horizon <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{2}-l_{\infty}$</tex> performance in the mean square. By using the Lyapunov stability theory, a sufficient condition is proposed to guarantee the existence of the desired estimator. An illustrative simulation example is given to verify the effectiveness and correctness of the proposed design scheme.