A stability result for 'separable' nonlinear discrete systems

Open-loop linearization of non-linear discrete input-output systems through simplification algorithms

“…We introduce the δǫ-operator to deal with cross-products among input and output signals, which acts upon a pair of sequences. This initially appeared in [9] and has been examined in [17], [16]. Let y(t), u(t) be real sequences, defined over the set of integers Z and let F be the set of causal sequences.…”

Regional stability of two‐dimensional nonlinear polynomial Fornasini‐Marchesini systems

“…Although DOA estimation for nonlinear systems in the 1D context has been investigated in several works using different approaches including linear matrix inequality (LMI) and sum‐of‐squares techniques (see, for example, the works), to the best of the authors' knowledge, the estimation of the DOA of 2D discrete‐time systems represented by a nonlinear polynomial FM model has not yet been addressed in the literature. The motivation for studying this problem is that 2D polynomial FM models can be applied to represent a number of dynamic processes such as (i) the so‐called “separable” nonlinear discrete‐time systems that are used in the control analysis of nonlinear dynamics (see, for example, related works), (ii) some industrial processes (eg, water‐stream heating and air‐drying processes) described by the so‐called Darboux equation with some of its coefficients depending on the controlled variable, (iii) 2D bilinear systems under a linear state‐feedback control law, and (iv) iterative learning control of nonlinear polynomial systems using a 2D FM state‐space model setting. In addition, since a smooth nonlinear function can be approximated (with a desired accuracy) by a polynomial function, 2D polynomial FM systems can approximately represent 2D‐smooth nonlinear FM models.…”