Study of uncontrollable discrete bilinear systems

Hollis, P.; Murthy, D. N. P.

doi:10.1109/tac.1982.1102829

Cited by 5 publications

(4 citation statements)

References 4 publications

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“…Some research on controllability for continuous time bilinear systems has been made [2,11], where Lie group and Lie algebra play a key role as the main mathematical tools [12]. For discrete time bilinear systems, the related works are fewer in number [13][14][15][16][17][18][19][20][21][22][23]. Here, we only consider the controllability of the following discrete time bilinear system:…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

“…where x(k) ∈ R n is the state variable, v(k) ∈ R is a scalar, and B ∈ R n×n is a real matrix. Note that none of the existing literature [14][15][16][17][18][19][20][21][22][23][24] can clarify the controllability of (1). In particular, some necessary and sufficient conditions were obtained on the premise of rank(B) = 1 in [14][15][16] and a sufficient condition was presented to judge whether (1) is controllable under strong restrictions in [19].…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

“…Some research on controllability for continuous time bilinear systems has been made , where Lie group and Lie algebra play a key role as the main mathematical tools . For discrete time bilinear systems, the related works are fewer in number . Here, we only consider the controllability of the following discrete time bilinear system:

x (k + 1) = (I + v (k) B) x (k)

where

x (k) \in {double-struckR}^{n}

is the state variable,

v (k) \in double-struckR

is a scalar, and

B \in {double-struckR}^{n \times n}

is a real matrix.…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

“…Here, we only consider the controllability of the following discrete time bilinear system:

x (k + 1) = (I + v (k) B) x (k)

where

x (k) \in {double-struckR}^{n}

is the state variable,

v (k) \in double-struckR

is a scalar, and

B \in {double-struckR}^{n \times n}

is a real matrix. Note that none of the existing literature can clarify the controllability of . In particular, some necessary and sufficient conditions were obtained on the premise of r a n k ( B ) = 1 in and a sufficient condition was presented to judge whether is controllable under strong restrictions in .…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

See 3 more Smart Citations

Study of a Class of Almost‐controllable Discrete‐time Bilinear Systems

Shen¹,

Zhu²

2014

Asian Journal of Control

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This paper studies the controllability of a class of time-invariant discrete-time bilinear systems. Although the system is not controllable in the whole space, there is a very large region where control is effective. Results show that the uncontrollable region of this kind of bilinear system has a Lebesgue measure of zero. In other words, for almost any initial state and any terminal state in the state space, the former can be transferred to the latter. Further, a necessary condition for near controllability is presented. Therefore, the results in this paper unify and generalize the corresponding conclusions in the literature.

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Section: Introduction and Statement Of Problemmentioning

confidence: 99%

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

x (k + 1) = (I + v (k) B) x (k)

where

x (k) \in {double-struckR}^{n}

is the state variable,

v (k) \in double-struckR

is a scalar, and

B \in {double-struckR}^{n \times n}

is a real matrix.…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

“…Here, we only consider the controllability of the following discrete time bilinear system:

x (k + 1) = (I + v (k) B) x (k)

where

x (k) \in {double-struckR}^{n}

is the state variable,

v (k) \in double-struckR

is a scalar, and

B \in {double-struckR}^{n \times n}

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

See 2 more Smart Citations

Study of a Class of Almost‐controllable Discrete‐time Bilinear Systems

Shen¹,

Zhu²

2014

Asian Journal of Control

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Suboptimal regulation of a class of bilinear interconnected systems on finite time-sliding planning horizons

Soto

Sen

1990

Mathematical and Computer Modelling

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This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.

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A Variable-structure Model for Policy Formulation of Mineral Resources Systems

Chu¹

1988

IFAC Proceedings Volumes

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Study of uncontrollable discrete bilinear systems

Cited by 5 publications

References 4 publications

Study of a Class of Almost‐controllable Discrete‐time Bilinear Systems

Study of a Class of Almost‐controllable Discrete‐time Bilinear Systems

Suboptimal regulation of a class of bilinear interconnected systems on finite time-sliding planning horizons

A Variable-structure Model for Policy Formulation of Mineral Resources Systems

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