Inners and Stability of Dynamic Systems

Jury, E.I.; Stark, Lawrence; Krishnan, V. V.

doi:10.1109/tsmc.1976.4309436

Cited by 75 publications

(130 citation statements)

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“…The minimal polynomial associated with state x r , and defined in Definition 3, is the same as the characteristic polynomial of the matrix J r appearing in eq. (8). The final value of x r , i.e., φ r can be computed based on the coefficients of the minimal polynomial of x r , and on the successive values of x r as described in eq.…”

Section: Decentralised Final Value Theoremmentioning

confidence: 99%

“…Using the Jury stability criterion for polynomials [8], we can check whether the polynomial defined in eq. (10) possesses at least an unstable root, i.e., a root, different form 1 and such that its magnitude is larger or equal to 1.…”

Section: Decentralised Final Value Theoremmentioning

confidence: 99%

“…Remark 3: A consequence of Theorem 1 is that the roots of q r (t) = 0 are the eigenvalues of the Jordan matrix J r appearing in (8).…”

Section: Decentralised Final Value Theoremmentioning

confidence: 99%

See 2 more Smart Citations

Decentralised final value theorem for discrete-time LTI systems with application to minimal-time distributed consensus

Yuan

Stan

Shi

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-In this study, we consider an unknown discretetime, linear time-invariant, autonomous system and characterise, the minimal number of discrete-time steps necessary to compute the asymptotic final value of a state. The results presented in this paper have a direct link with the celebrated final value theorem. We apply these results to the design of an algorithm for minimal-time distributed consensus and illustrate the results on an example.

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Section: Decentralised Final Value Theoremmentioning

confidence: 99%

Section: Decentralised Final Value Theoremmentioning

confidence: 99%

See 1 more Smart Citation

Decentralised final value theorem for discrete-time LTI systems with application to minimal-time distributed consensus

Yuan

Stan

Shi

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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“…Stability can be readily investigated via transfer functions and we will exploit Jury's Inners approach to conduct the analysis, Jury (1974). This transfer function of the retailers order rate is…”

Section: Stability Analysismentioning

confidence: 99%

Altruistic behaviour in a two-echelon supply chain with unmatched proportional feedback controllers

Disney

Hosoda

2009

IJISTA

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We study a two echelon supply chain with first order autoregressive demand and unit replenishment lead-times. Each echelon of the supply chain uses conditional expectation to generate Minimum Mean Squared Error (MMSE) forecasts. Both echelons use these forecasts inside the "Order-Up-To" policy to generate replenishment orders. We investigate three different scenarios: The first is when each echelon aims to minimize their own local inventory holding and backlog costs. The second scenario is concerned with an altruistic retailer who is willing and able to sacrifice some of his own performance for the benefit of the total supply chain. The retailer does this by smoothing the demand placed on the manufacturer by using a matched proportional controller in the inventory and WIP feedback loops. The third scenario is concerned with an altruistic retailer with two, unmatched, controllers. The matched controller case out-performs the traditional case by 14.1%; the unmatched controller case outperforms the matched controller case by 4.9%.

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“…Once the designer has specified Q, H and R, representing different weightings in (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), the optimal closed-loop system will be (1-15a) y(t) -Cx(t) (1-15b)…”

mentioning

confidence: 99%

Approximate Linear Regulator and Kalman Filter

Shieh¹,

Wai²

1980

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Two central problems in modern control theory are the controller design problem: which deals with designing a control law for the dynamical system, and the state estimation problem (observer design problem): which deals with computing an estimate of the states of the dynamical system. The Linear Quadratic Regulator (LQR) and Kalman Filter (KF) solves these problems respectively for linear dynamical systems in an optimal manner, i.e., LQR is an optimal state feedback controller and KF is an optimal state estimator. In this note, we will be discussing the basic concepts, derivation, steady-state analysis, and numerical implementation of the LQR and KF.

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Inners and Stability of Dynamic Systems

Cited by 75 publications

References 0 publications

Decentralised final value theorem for discrete-time LTI systems with application to minimal-time distributed consensus

Decentralised final value theorem for discrete-time LTI systems with application to minimal-time distributed consensus

Altruistic behaviour in a two-echelon supply chain with unmatched proportional feedback controllers

Approximate Linear Regulator and Kalman Filter

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