A differential-algebraic condition for controllability and observability of time varying linear systems

Szigeti, Ferenc

doi:10.1109/cdc.1992.371050

Cited by 51 publications

(16 citation statements)

References 3 publications

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“…The observability characterized in terms of known system coefficient matrices was investigated in Silverman and Meadows (1967). An algebraic rank condition, which relies on expanding the time varying structure matrix in the generated Lie algebra, with respect to a basis was provided by Szigeti (1992). In particular, it is proven that, under a differential-algebraic condition for the time-dependent coefficients, observability is equivalent to a multivariable Kalman condition.…”

Section: Introductionmentioning

confidence: 99%

A necessary and sufficient condition for total observability of discrete-time linear time-varying systems

et al. 2017

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This paper deals with the total observability problem of discrete-time linear time-varying systems. In particular, a review and suitable analysis of the state-of-the-art of this emerging area are provided. Subsequently, the total observability problem of discrete-time linear time-varying systems is transformed into the one of checking the rank of a convex sum of matrices. As a result, a new total observability test is proposed, along with a suitable computational strategy. The final part of this paper shows examples regarding observability analysis that clearly exhibit the benefits of using the proposed approach.

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Section: Introductionmentioning

confidence: 99%

A necessary and sufficient condition for total observability of discrete-time linear time-varying systems

et al. 2017

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“…As for controllability and reachability, studies for low-order switched linear systems have been presented in Loparo, Aslanis & IIajek (1987) and Xu & Antsaklis (1999). Some sufficient conditions and necessary conditions for controllability were presented in Ezzine & Haddad (1989) and Szigeti (1992) for switched linear control systems under the assumption that the switching sequence is fixed a priori. The complexity of stability and controllability of hybrid systems was addressed in Blondel & Tsitsiklis (1999).…”

Section: Introductionmentioning

confidence: 99%

Controllability and reachability criteria for switched linear systems

2002

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“…Work on identification/filtering of hybrid systems first appeared in the seventies (see [19] for a review). More recent works consider variations of Problem 1 in which the model parameters, the discrete state and/or the switching mechanism are known, and concentrate on the analysis of the observability of the hybrid state [2], [4], [9], [11], [18], [21], [22] and the design of hybrid observers [1], [3], [7], [8], [10], [12], [14], [16], [17], [20].…”

Section: Problemmentioning

confidence: 99%

Identification of PWARX hybrid models with unknown and possibly different orders

Vidal

2004

Proceedings of the 2004 American Control Conference

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Abstract-We consider the problem of identifying the orders and the model parameters of PWARX hybrid models from noiseless input/output data. We cast the identification problem in an algebraic geometric framework in which the number of discrete states corresponds to the degree of a multivariate polynomial p and the orders and the model parameters are encoded on the factors of p. We derive a rank constraint on the input/output data from which one can estimate the coefficients of p. Given p, we show that one can estimate the orders and the parameters of each ARX model from the derivatives of p at a collection of regressors that minimize a certain objective function. Our solution does not require previous knowledge about the orders of the ARX models (only an upper bound is needed), nor does it constraint the orders to be equal. Also the switching mechanism can be arbitrary, hence the switches need not be separated by a minimum dwell time. We illustrate our approach with an algebraic example of a switching circuit and with simulation results in the presence of noisy data.

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A differential-algebraic condition for controllability and observability of time varying linear systems

Cited by 51 publications

References 3 publications

A necessary and sufficient condition for total observability of discrete-time linear time-varying systems

A necessary and sufficient condition for total observability of discrete-time linear time-varying systems

Controllability and reachability criteria for switched linear systems

Identification of PWARX hybrid models with unknown and possibly different orders

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