On nonlinear robust state estimation for generalized Persidskii systems

Annular short-time stability of generalized Persidskii systems

“…Following [28], [16], [22], [23], the stability analysis of (2) can be performed using a Lyapunov function…”

“…The considered class of nonlinear dynamics in this paper is called the generalized Persidskii systems, which have been extensively studied in the context of neural networks [15], biological models [16], and power systems [17], and whose original form was introduced in [18], [19], [20]. Recently the conditions of input-to-state stability, input-tooutput stability, and convergence, as well as the synthesis of a state observer have been established in [21], [16], [22], [23] for generalized Persidskii models. Note that most existing approaches to synthesizing Lyapunov functions for stability analysis in nonlinear dynamics involve various canonical forms of the studied differential equations, such as Lur'e systems [24], homogeneous models [25], Persidskii systems [18], and Lipschitz dynamics, and the presence of nonlinearities leads to that the established stability conditions can be rather complicated.…”

State observer design for bilinear Persidskii systems

“…The model we consider in this paper is a generalization of the important class of Persidskii systems, first introduced in [1], [13] for stability analysis, also related with Lur'e systems studied in the absolute stability theory [17], [9]. Thus, the advantage of Persidskii systems consists in the existence of a well-investigated form of candidate Lyapunov functions, which was used in many cases [6], [12], [11], often resulting in stability conditions that can be formulated in the form of linear matrix inequalities. Moreover, this class of models has been found valuable in representing many physical and biological phenomena, and therefore, it has been studied from many viewpoints, including that of IOS-stability [12].…”

“…Thus, the advantage of Persidskii systems consists in the existence of a well-investigated form of candidate Lyapunov functions, which was used in many cases [6], [12], [11], often resulting in stability conditions that can be formulated in the form of linear matrix inequalities. Moreover, this class of models has been found valuable in representing many physical and biological phenomena, and therefore, it has been studied from many viewpoints, including that of IOS-stability [12]. In this paper, we consider a more significant generalization of this class of systems, motivated by biological and physical examples [8], [5], [3], where some new classes of nonlinearities are taken into account, in particular allowing for the addition of bilinear cross-products.…”

“…The goal of this work is to consider a more complex Persidskii-like dynamics as in [12], which include bilinear terms (products of the state components and the nonlinearities or inputs), and design a state observer using the IOS theory. The existing results in the literature study only particular classes of bilinear systems, see [14] and references therein.…”