On the Stability of 2-D Continuous Systems

Abstract In this paper the definition of bounded-input bounded-output stability of 2-D continuous systems is introduced. A method of checking this stability condition is discussed. Also it is shown that by using one-variable reactance transformation (or spectral transformation) to obtain the 2-D continuous transfer function, stability is, in general, not preserved. This is in contrast to the 2-D discrete transfer function. The effect of double bilinear transformation from the 2-D continuous transfer function to the corresponding discrete one is discussed. It is shown by an example that the impulse responses of both, continuous and discrete transfer functions are not preserved. This is in contrast to the 1-D case . Future research in testing the stability condition in the s 1 , s 2 - biplane is mentioned.