Generalized regularity and regularizability of rectangular descriptor systems

Duan, Guang‐Ren; Chen, Yan

doi:10.1007/s11768-005-5313-3

Cited by 13 publications

(3 citation statements)

References 16 publications

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“…Fruitful basic researches of the rectangular descriptor systems are listed, for instance, impulse controllability and impulse observability [6,7], generalized regularity [8], the problems of stabilization [9] and observer design [10]. Lin et al [11] discussed the fuzzy normalization and stabilization for nonlinear rectangular descriptor systems.…”

Section: Introductionmentioning

confidence: 99%

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

2022

Asian Journal of Control

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In this article, the indefinite linear quadratic (LQ) optimal control problem for discrete time-varying rectangular descriptor systems is investigated, in which the indefinite weight matrices are considered in the quadratic cost function. With a suite of equivalent transformations, the indefinite LQ problem for discrete time-varying rectangular descriptor systems can be substituted by an equivalent indefinite LQ problem for standard state space systems. Then, the transformed equivalent indefinite LQ problem is solved by establishing a dual Krein space model, and the optimal control and optimal cost value are obtained by invoking the Kalman filter of Krein space. The form of state feedback optimal control corresponding to the original system is given. Next, to guarantee the dynamic part for the resulting optimal closed-loop system has a unique solution, some necessary and sufficient conditions are proposed. Finally, a numerical example is carried out to demonstrate the availability of established results.

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Section: Introductionmentioning

confidence: 99%

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

2022

Asian Journal of Control

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“…Rectangular descriptor systems, where the number of equations and state variables may not be equal, have broader descriptions and more complex behaviors than square descriptor systems [17]. So far, the results for rectangular descriptor systems are extremely abundant, like generalized regularity and regularizability, impulse controllability and observability, estimation and observer design [18]- [23]. What's more, a new feedback structure to stabilize rectangular descriptor systems by dynamic output feedback (dynamic compensator) plus state feedback is proposed in [26].…”

Section: Introductionmentioning

confidence: 99%

Stabilization for Rectangular Descriptor Fractional Order Systems

2019

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This paper focuses on the stabilization problem for rectangular descriptor fractional order systems (FOSs) with 0 < α ≤ 1. Firstly, a fractional order dynamic compensator is constructed to make the closed-loop systems square descriptor FOSs. Secondly, two types of input signals of the compensator are considered, which are state input signal case and output input signal case. Thirdly, a necessary and sufficient condition is proposed for the state input signal case, while a new method of controller design is given for the output input signal case in which the output matrix of the system need not to be full row rank, which reduces the conservativeness of existing methods. Finally, an efficient iterative algorithm for solving the resultant matrix inequalities is proposed, and a numerical example is offered to verify the advantage and feasibility of the results.

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“…No special assumptions are made on the matrix pencil sE − A, in the most general case it can be rectangular (n d = n eq ). This type of systems has attracted much attention during the last two decades (Geerts (1993), Ishihara and Terra (2001), Hou and Muller (1999), Hou (2004), Zhang (2006), Duan and Chen (2007), . .…”

Section: Introductionmentioning

confidence: 99%