Continuous observer design for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements

Abstract

In this paper, continuous observer is designed for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements. The time delay may be larger or less than the sampling intervals. The sampled and delayed measurements are used to update the observer whenever they are available. Sufficient conditions are presented to ensure global exponential stability of the observation errors by constructing a Lyapunov-Krasovskii function. A numerical example is given to illustrate the effectiveness of the proposed methods.

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

“…However, small γ may yield chattering phenomenon. In other works, the authors addressed this problem clearly. Motivated by the ideas of the above papers, the chattering problem may be solved by applying the similar methods.…”

Global sampled‐data output‐feedback stabilization for nonlinear systems with unknown measurement sensitivity

“…Now, usingẑ i (t k ) for i = 2, … , n given by (11), the sampled-data output-feedback control law is constructed as follows:…”

“…Without doubt, the accuracy of the measurement output y(t) plays a key role in output-feedback design for system (1). 1,2 When the measurement sensitivity is a known constant, eg, (t) ≡ 1, the global output-feedback stabilization problem of system (1) has been well addressed in the literature under various conditions on f i (x(t), u(t), t) (see, for instance, other related works [3][4][5][6][7][8][9][10][11][12] , as well as the references therein). Unfortunately, in practice, the measurement sensitivity (t) is in general time-varying as pointed out in the works of Carr 13 and Chen et al 14 ; the unknown time-varying derivation of (t) from the desired nominal value nominal = 1 is known as (sensor) sensitivity error.…”

“…[14][15][16] A practical example can be found in the work of Lantto,17(p56) in which the displacement sensor in a magnetic bearing suspension system suffers from 10% sensitivity error, that is, the output of the sensor might differ from the real value with 10% variation. Notably, most of existing results [3][4][5][6][7][8][9][10][11] are inapplicable to system (1) because a common assumption in other works [3][4][5][6][7][8][9][10][11] is that the relationship between the state x 1 (t) and the output y(t) is explicitly clear and available. Although there are some works [18][19][20] dealing with output-feedback design for nonlinear systems with unknown output function y(t) = h(x 1 (t)), the methods in the works of Zhai and Qian 18 and Li et al 19 are not applicable to system (1) due to the requirement of differentiability of y(t) in t 18 or Lipschitz continuity of h(x 1 ) in x 1 19,20 ; both requirements may not satisfied by the output of system (1) because the measurement sensitivity (t) is only a continuous function.…”

Sampled‐data control of a class of uncertain switched nonlinear systems in nonstrict‐feedback form

“…Du et al gave the stability analysis of a continuous second‐order finite‐time control system under sampled‐data control. Shen et al designed a continuous observer for a class of multi‐output nonlinear systems with multirate sampled and delayed output measurements.…”