A survey of interval observers design methods and implementation for uncertain systems

What is it about?

The goal of the interval observers is to deal with the large but bounded uncertainties and disturbances by determining certain interval (upper and lower estimates) for the system states at each time instant. The mean of the interval that should be minimized can be considered as the point-wise estimate whereas the interval width provides the admissible deviation from that value. Thus, an interval estimation error bound is provided at any time instant that converges to zero in the absence of exogenous signals. Interval observers can be used in a wide range of applications because of its reliable uncertainties propagation such as robust control of linear and non-linear systems, fault detection and isolation, anti-disturbance controller design and so on. This paper presents some of the basic concepts and recent results obtained to design interval observers for uncertain systems like discrete-time, continuous-time, Linear Parameter Varying (LPV) systems and multiagent/interconnected systems. In addition, it also presents a brief discussion of the main approaches with some future recommendations.

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Photo by Adli Wahid on Unsplash

Photo by Adli Wahid on Unsplash

Why is it important?

This brief proposes a new method to design interval state estimator for LPV systems subject to state disturbances and measurement noises using the observability matrix. The design of the standard interval observer is usually based on the cooperativity of the system error dynamics which is hard to satisfy. However, the new method developed in this brief relaxes such a restrictive constraint. The proposed method uses the previous input-output values along with the observability matrix to generate a guaranteed interval for the system states. Compared with the existing techniques, the proposed approach is simple and less restrictive. The finite-time convergence is provided to show the boundedness of the interval vector and error dynamics.