Positive Realization Problem of 1D Descriptor Linear Systems

Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini modelThe realization problem for positive multi-input and multi-output (MIMO) linear hybrid systems with the form of second Fornasini-Marchesini model is formulated and a method based on the state variable diagram for finding a positive realization of a given proper transfer matrix is proposed. Sufficient conditions for the existence of the positive realization of a given proper transfer matrix are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.

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Fault diagnosis for discrete-time descriptor linear systems

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2015.09.695 ◽

2015 ◽

Vol 48 (21) ◽

pp. 1238-1243 ◽

Cited By ~ 1

Author(s):

G.-L. Osorio-Gordillo ◽

M. Darouach ◽

C.-M. Astorga-Zaragoza ◽

L. Boutat-Baddas

Keyword(s):

Fault Diagnosis ◽

Linear Systems ◽

Discrete Time ◽

Descriptor Linear Systems

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Fault estimation for descriptor linear systems based on the generalised dynamic observer

International Journal of Systems Science ◽

10.1080/00207721.2018.1503357 ◽

2018 ◽

Vol 49 (11) ◽

pp. 2398-2409

Author(s):

Gloria Osorio-Gordillo ◽

Carlos Astorga-Zaragoza ◽

Abraham Pérez Estrada ◽

Rodolfo Vargas-Méndez ◽

Mohamed Darouach ◽

...

Keyword(s):

Linear Systems ◽

Fault Estimation ◽

Descriptor Linear Systems ◽

Dynamic Observer

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Robust model reference control for second-order descriptor linear systems subject to parameter uncertainties

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211045055 ◽

2021 ◽

pp. 014233122110450

Author(s):

Guang-Tai Tian ◽

Guang-Ren Duan

Keyword(s):

Linear Systems ◽

Tracking Error ◽

Sufficient Conditions ◽

Second Order ◽

Parameter Uncertainties ◽

Robust Controller ◽

Model Reference ◽

Robust Model ◽

Robust Compensation ◽

Descriptor Linear Systems

This paper is devoted to designing the robust model reference controller for uncertain second-order descriptor linear systems subject to parameter uncertainties. The parameter uncertainties are assumed to be norm-bounded. The design of a robust controller can be divided into two separate problems: a robust stabilization problem and a robust compensation problem. Based on the solution of generalized Sylvester matrix equations, we obtain some sufficient conditions to guarantee the complete parameterization of the robust controller. The parametric forms are expressed by a group of parameter vectors which reveal the degrees of freedom existing in the design of the compensator and can be utilized to solve the robust compensation problem. In order to reduce the effect of parameter uncertainties on the tracking error vector, the robust compensation problem is converted into a convex optimization problem with a set of linear matrix equation constraints. A simulation example is provided to illustrate the effectiveness of the proposed technique.

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