State Observers for Systems Subject to Bounded Disturbances Using Quadratic Boundedness

Abstract

Quadratic boundedness is adopted to construct state observers for linear, piecewise linear, and Lipschitz nonlinear systems subject to bounded disturbances. Upper bounds on the estimation error are derived by exploiting quadratic boundedness and a design method based on linear matrix inequalities is proposed to minimize such bounds. Simulation results are provided to show the effectiveness of the proposed approach.

A survey on tracking control of unmanned underwater vehicles: Experiments-based approach

“…Hence, a saturated observation-based control law can be considered as a potential solution. In line with this idea, different observer structures have been proposed in the literature (see Zemouche et al (2019), Alessandri and Boem (2020), Wang et al (2020a), for example).…”

Continuous–Discrete Observation-Based Robust Tracking Control of Underwater Vehicles: Design, Stability Analysis, and Experiments

“…Accordingly, different observer design techniques have been proposed in the literature for nonlinear systems, as follows: An improved high-gain nonlinear observer was proposed to decrease the gain power of a well-known classical high-gain observer by exploiting linear matrix inequalities (LMI) and a compromise index concept in [13]. Similarly, a state observer based on an LMI technique was developed in [15] to compensate for the effect of bounded disturbances. The extension of this approach to marine robots requires knowledge of disturbance bounds.…”

Observer-based control for a class of hybrid linear and nonlinear systems

“…Such conditions point out that a delay with respect to the current available information is required to accomplish a correct evaluation of the system mode (see also [1]). Indeed, here we consider the case with no delay permitted in generating the control and propose to perform the estimation of the mode with a mode predictor [3]. Switching-gain observers are analyzed in [19].…”

“…Of course, this would cause a delay in generating the control action. Instead, we will exploit the knowledge of the discrete state dynamics by using a mode predictor that estimates the mode one-step ahead based also on the current estimates, i.e., λ t =F t, y t ,x t , u t−1 ,λ t−1 (3) whereF :…”

“…A reduction of the number of constraints in ( 9) is crucial to ensure the LMI feasibility. In the worst case, we have q 3 LMIs, but such a number can be reduced in general. If the instantaneous value of the switching mode is known in real time, we have to satisfy (9) with i = j, and hence to deal with q 2 LMIs.…”