Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

Abstract

SUMMARYThis paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time-varying delay and the one-sided Lipschitz condition. By constructing the novel Lyapunov-Krasovskii functional while utilizing the free-weighting matrices approach, the one-sided Lipschitz condition and the quadratic inner-bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time-varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method.

Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

“…Further conclusions on this topic can be found in References . Subsequently, the observer design schemes for nonlinear time‐delay systems in terms of one‐sided Lipschitz condition have been reported in References .…”

“…In this case, a state observer is usually employed to accurately reconstruct the state variables of the process. In recent years, a subject of tremendous research activities has been focused on observer design problem for nonlinear time‐delay systems …”

“…In Reference , the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time‐varying delay and one‐sided Lipschitz condition is investigated. In Reference , a novel nonlinear observer‐design approach to one‐sided Lipschitz nonlinear systems in the presence of output delays is presented.…”

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

“…In the works of Nguyen and Trinh, nonlinear reduced‐order observers were introduced to one‐sided Lipschitz discrete‐time and continuous‐time systems with time‐varying delay quite recently. The linear matrix inequality (LMI) conditions for the observer synthesis problems of one‐sided Lipschitz nonlinear systems with interval time‐varying delay and uncertainties are presented in the work of Dong et al However, the considered nonlinear models in these works are all standard systems.…”

Robust observer design for uncertain one‐sided Lipschitz systems with disturbances

“…Because the one‐sided Lipschitz condition is in a weighted bilinear form, which poses challenges in designing nonlinear observers, the quadratically inner‐bounded condition was introduced in the work of Abbaszadeh and Marquez as a useful solution to derive tractable conditions for observer designs for one‐sided Lipschitz nonlinear systems. The problem of designing observers for nonlinear systems satisfying both the one‐sided Lipschitz condition and the quadratically inner‐bounded condition has attracted great attention from researchers with many results reported in the literature …”