Abstract
This paper deals with the global asymptotic stability (GAS) of the fixed-point two-dimensional (2D) Lipschitz nonlinear digital filter (LNDF) in Fornasini–Marchesini second local state-space (FMSLSS) model with 2’s complement overflow. In particular, the 2D system under study involves intrinsic system nonlinearities as well as nonlinearities due to overflow. New conditions for verifying the GAS of such LNDFs is developed in this paper. The criterion utilizes Lyapunov method and the properties of overflow arithmetic and Lipschitz nonlinearities. A criterion for the overflow stability of 2D systems (without intrinsic system nonlinearities) is also brought out. The obtained criteria are also applicable to digital filters with other frequently used overflow arithmetic (namely, saturation, zeroing, and triangular). The results presented in this paper can be used directly as criteria for elimination of overflow oscillations in 2D systems. The obtained results are compared with existing results.
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Singh, S., Kar, H. Stability of 2D Lipschitz Nonlinear Digital Filters in Fornasini–Marchesini Second Model with Overflow Arithmetic. J Control Autom Electr Syst 34, 50–59 (2023). https://doi.org/10.1007/s40313-022-00930-1
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DOI: https://doi.org/10.1007/s40313-022-00930-1