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Universidad de la Costa, CUC. Calle 58 # 55 - 66. Barranquilla, Colombia. 336 22 00. repositorioredicuc@cuc.edu.co. Corporación Universidad de la Costa.

Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator

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Average reachability of continuous-time Markov jump linear (718.3Kb)
Date
2016
Author
Roa Narvaez, Alfredo Rafael
Fontoura Costa, Eduardo
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URI: http://hdl.handle.net/11323/1286

Abstract

. In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a testable condition, we introduce a set of reachability matrices for this class of systems and employ invariance properties of the null space of the noise coefficient matrices to show that the system is reachable if and only if these matrices are of full rank. We also show for reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear minimum mean square state estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, the average boundedness of the error covariance matrix is invariant to a type of perturbation in the noise model, meaning that the estimates are not overly sensitive, which consists in a property that is desirable in applications and sometimes referred to as stability of the estimator.
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Universidad de la Costa, CUC

  • Calle 58 # 55 - 66. Barranquilla, Colombia

  • 336 22 00

  • repositorioredicuc@cuc.edu.co

Corporación Universidad de la Costa CUC, Personería Jurídica con Resolución No. 352 del 23 de abril de 1971 y reconocida como Universidad mediante resolución 3235 del 28 de marzo de 2012 expedida por el MEN. Institución de Educación Superior sujeta a inspección y vigilancia por el Ministerio de Educación Nacional.

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