Optimal ${\cal H}_{2}$ Filtering in Networked Control Systems With Multiple Packet Dropout

Abstract

This note studies the problem of optimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> filtering in networked control systems (NCSs) with multiple packet dropout. A new formulation is employed to model the multiple packet dropout case, where the random dropout rate is transformed into a stochastic parameter in the system's representation. By generalization of the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm definition, new relations for the stochastic -norm of a linear discrete-time stochastic parameter system represented in the state-space form are derived. The stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm of the estimation error is used as a criterion for filter design in the NCS framework. A set of linear matrix inequalities (LMIs) is given to solve the corresponding filter design problem. A simulation example supports the theory.