Temporal Linear System Structure

Willigenburg, L.G. van; Koning, W. L. De

doi:10.1109/tac.2008.921033

Cited by 13 publications

(38 citation statements)

References 13 publications

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“…The description and detection of temporal linear system structure require considering conventional as well as piecewise constant rank systems (PCR systems) [7,8]. PCR systems also arise as a result of balanced truncation of time-varying linear systems [9].…”

Section: Introductionmentioning

confidence: 99%

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Temporal and differential stabilizability and detectability of piecewise constant rank systems

Willigenburg

Koning

2011

Optim Control Appl Methods

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SUMMARYIn a past note we drew attention to the fact that time-varying continuous-time linear systems may be temporarily uncontrollable and unreconstructable and that this is vital knowledge to both control engineers and system scientists. Describing and detecting the temporal loss of controllability and reconstructability require considering piecewise constant rank (PCR) systems and the differential Kalman decomposition. In this note for conventional as well as PCR systems measures of temporal and differential stabilizability and detectability are developed. These measures indicate to what extent the temporal loss of controllability and reconstructability may lead to temporal instability of the closed-loop system when designing a static state or dynamic output feedback controller. It is indicated how to compute the measures from the system matrices. The importance of our developments for control system design is illustrated through three numerical examples concerning LQ and LQG perturbation feedback control of a non-linear system about an optimal control and state trajectory.

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Section: Introductionmentioning

confidence: 99%

“…PCR systems also arise as a result of balanced truncation of time-varying linear systems [9]. The differential Kalman decomposition (d-Kalman decomposition) developed in [7,8] detects temporal linear system structure. Among other things it detects the intervals where the temporal loss of controllability or reconstructability occurs.…”

Section: Introductionmentioning

confidence: 99%

Temporal and differential stabilizability and detectability of piecewise constant rank systems

Willigenburg

Koning

2011

Optim Control Appl Methods

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“…For control system design this is vital information since this structure reveals the temporal loss of controllability and reconstructability of the linearized system. They in turn may lead to temporal instability of a closed-loop control system [3], [4]. Recently we investigated these issues for continuous-time systems assuming continuous-time control.…”

Section: Introductionmentioning

confidence: 99%

“…The fact that discrete-time is not dense, as opposed to continuous-time, causes some major differences. In continuous-time our investigation required the introduction of piecewise constant rank systems and the differential Kalman decomposition [3], [4]. In discretetime their counterparts are discrete-time linear systems with variable state dimensions and the j-step, k-step Kalman decomposition [11].…”

Section: Introductionmentioning

confidence: 99%

“…Temporal uncontrollability/unreachability and temporal unreconstructability/ unobservability of linear time-varying systems was introduced and investigated in continuous-time [3], [4] and in discrete-time [11]. Intuitively, temporal stabilizability and temporal detectability are associated properties that apply over intervals where the system is temporal uncontrollable/unreachable and temporal unreconstructable/unobservable respectively.…”

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confidence: 99%

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Temporal and One-Step Stabilizability and Detectability of Time-Varying Discrete-Time Linear Systems

Willigenburg¹,

Koning²

2013

IFIP Advances in Information and Communication Technology

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Abstract. Time-varying discrete-time linear systems may be temporarily uncontrollable and unreconstructable. This is vital knowledge to both control engineers and system scientists. Describing and detecting the temporal loss of controllability and reconstructability requires considering discrete-time systems with variable dimensions and the j-step, k-step Kalman decomposition. In this note for linear discrete-time systems with variable dimensions measures of temporal and one-step stabilizability and detectability are developed. These measures indicate to what extent the temporal loss of controllability and reconstructability may lead to temporal instability of the closed loop system when designing a static state or dynamic output feedback controller. The measures are calculated by solving specific linear quadratic cheap control problems.

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Adaptive control and signal processing literature survey (No. 5)

2008

Adaptive Control & Signal

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In order to keep readers up to date, the journal will contain a list of recently published journal articles relevant to the fields of adaptive control and signal processing six times a year. This list is compiled from a wide range of journals. Please note that even though the list has been broadly categorized these classifications are by no means strict, and are there to assist the reader. Please also note that inclusion in the list is not an endorsement of a paper's quality. If you have any suggestions or comments, please

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Temporal Linear System Structure

Cited by 13 publications

References 13 publications

Temporal and differential stabilizability and detectability of piecewise constant rank systems

Temporal and differential stabilizability and detectability of piecewise constant rank systems

Temporal and One-Step Stabilizability and Detectability of Time-Varying Discrete-Time Linear Systems

Adaptive control and signal processing literature survey (No. 5)

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