Steady-state feedforward compensation for discrete time multivariable systems

This paper proposes a new algorithm to estimate the optimal steady-state Kalman filter gain of a linear, discrete-time, time-invariant stochastic system from nonoptimal Kalman filter residuals. The system matrices are known, but the covariances of the white process and measurement noises are unknown. The algorithm first derives a moving average (MA) model which relates the optimal and nonoptimal residuals. The MA model is then approximated by inverting a long autoregressive (AR) model. From the MA parameters the Kalman filter gain is calculated. The estimated gain in general is suboptimal due to the approximations involved in the method and a finite number of data. However, the numerical example shows that the estimated gain could be near optimal.

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Sojourn Times in A Queueing System with Breakdowns and General Retrial Times

Mathematics ◽

10.3390/math9222882 ◽

2021 ◽

Vol 9 (22) ◽

pp. 2882

Author(s):

Ivan Atencia ◽

José Luis Galán-García

Keyword(s):

Steady State ◽

Discrete Time ◽

Queueing System ◽

Retrial Queue ◽

Stochastic Decomposition ◽

Discrete Time System ◽

Main Research ◽

Extensive Analysis ◽

Complete Study ◽

Number Of Customers

This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the stationary distributions of the number of customers in the orbit and in the system by applying the generation function (GF). We provide the stochastic decomposition law and the application bounds for the proximity between the steady-state distributions for the queueing system under consideration and its corresponding standard system. We developed recursive formulae aimed at the calculation of the steady-state of the orbit and the system. We proved that our discrete-time system approximates M/G/1 with breakdowns and repairs. We analyzed the busy period of an auxiliary system, the objective of which was to study the customer’s delay. The stationary distribution of a customer’s sojourn in the orbit and in the system was the object of a thorough and complete study. Finally, we provide numerical examples that outline the effect of the parameters on several performance characteristics and a conclusions section resuming the main research contributions of the paper.

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Optimal guaranteed cost filtering for Markovian jump discrete-time systems

Mathematical Problems in Engineering ◽

10.1155/s1024123x04108016 ◽

2004 ◽

Vol 2004 (1) ◽

pp. 33-48 ◽

Cited By ~ 13

Author(s):

Magdi S. Mahmoud ◽

Peng Shi

Keyword(s):

Steady State ◽

Discrete Time ◽

Estimation Error ◽

Linear Matrix ◽

State Estimator ◽

Markovian Jump ◽

Markovian Jump Parameters ◽

Discrete Time Systems ◽

Linear State ◽

Time Systems

This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

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Steady-state errors in discrete-time control systems

[1992] Proceedings of the 31st IEEE Conference on Decision and Control ◽

10.1109/cdc.1992.371365 ◽

2005 ◽

Author(s):

I.W. Sandberg ◽

L.Y. Xu

Keyword(s):

Steady State ◽

Control Systems ◽

Discrete Time ◽

Time Control

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