New criteria for asymptotic stability of one- and multidimensional state-space digital filters in fixed-point arithmetic

This paper addresses the problem of global asymptotic stability of one-dimensional (1-D) and multidimensional (m-D) digital filters with any combination of overflow and quantization nonlinearities. The stability analysis is carried out using 1-D and m-D state-space representations. The approach introduced allows one to determine the stability behavior of single-input single-output systems with overflow and quantization nonlinearities. The new criteria, based on previous stability results of digital filters with quantization schemes, are applicable to all arithmetic schemes. For the first time, results concerning general state variable representations of 1-D and m-D digital filters with the naturally occurring combination of two's complement truncation quantization and overflow are reported. Furthermore, significantly improved stability regions are obtained for digital filters with roundoff nonlinearities