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Journal of Control Science and Engineering
Volume 2016, Article ID 4281786, 6 pages
Research Article

Study of the Convergence in State Estimators for LTI Systems with Event Detection

1Instituto Tecnológico Metropolitano (ITM), Medellín, Colombia
2Facultad IEE, Universidad Pontificia Bolivariana, Circular 1 No. 70-01, Medellín, Colombia
3Automation Department, Engineering Institute, UNAM, 4500 Mexico City, Mexico
4EAFIT University, Medellin, Colombia

Received 4 November 2015; Accepted 17 February 2016

Academic Editor: Hung-Yuan Chung

Copyright © 2016 Juan C. Posada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The methods frequently used to estimate the state of an LTI system require that the precise value of the output variable is known at all times, or at equidistant sampling times. In LTI systems, in which the output signal is measured through binary sensors (detectors), the traditional way of state observers design is not applicable even though the system has a complete observability matrix. This type of state observers design is known as passive. It is necessary, then, to introduce a new state estimation technique, which allows reckoning the state from the information of the variable’s crossing through a detector’s action threshold (switch). This paper seeks, therefore, to study the convergence in this type of estimators in finite time, allowing establishing, theoretically, whether some family of the proposed models can be estimated in a convergent way through the use of the estimation technique based on events.