Robust Filtering for 2-D Discrete-Time Switched Systems

Abstract

In this article, we study the robust filtering problem for 2-D switched systems with convex-bounded uncertainties. The studied switched system is formulated by Fornasini–Marchesini local state-space model, and system matrices depend affinely on convex-bounded uncertain parameters. We first derive synthesis results for 2-D switched systems, which extends the existing results and lays a foundation for the robust filter design. To design the robust filter, we transform the 2-D switched system into an equivalent difference-algebraic representation form. Using the equivalent representation and the parameter-dependent Lyapunov function approach, sufficient conditions are established for system stability, and 2-D stationary discrete-time linear filters are designed to ensure the prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> performance for all admissible uncertain parameters. Finally, a numerical example is presented to illustrate the obtained results.