Robust Performance Analysis of Linear Time-Invariant Uncertain Systems by Taking Higher-Order Time-Derivatives of the State

2006 ◽  
Author(s):  
Y. Ebihara ◽  
T. Hagiwara ◽  
D. Peaucelle ◽  
D. Arzelier
Keyword(s):  
Performance Analysis ◽  
Uncertain Systems ◽  
Linear Time ◽  
Higher Order ◽  
The State ◽  
Robust Performance ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Derivatives Of

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Complete moment convergence for the dependent linear processes with application to the state observers of linear-time-invariant systems

2020 ◽  
Vol 65 (4) ◽  
pp. 725-745
Author(s):  
Chao Lu ◽  
Chao Lu ◽  
Xuejun J Wang ◽  
Xuejun J Wang ◽  
Yi Wu ◽  
...  
Keyword(s):  
Linear Time ◽  
The State ◽  
Complete Moment Convergence ◽  
Linear Processes ◽  
Linear Time Invariant ◽  
Moment Convergence ◽  
State Observers ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Пусть $X_t=\sum_{j=-\infty}^{\infty}A_j\varepsilon_{t-j}$ - зависимый линейный процесс, где $\{\varepsilon_n, n\in \mathbf{Z}\}$ - последовательность $m$-обобщенных отрицательно зависимых ($m$-END) случайных величин с нулевым средним, которая стохастически доминируется случайной величиной $\varepsilon$, и пусть $\{A_n, n\in \mathbf{Z}\}$ - другая последовательность случайных величин с нулевым средним, обладающая свойством $m$-END. При подходящих условиях установлена полная моментная сходимость для зависимых линейных процессов. В частности, приведены достаточные условия полной моментной сходимости. В качестве приложения исследуется сходимость наблюдателей состояния для линейных стационарных систем.

Steady-State Optimal State and Input Observer for Discrete Stochastic Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Y. Park ◽  
J. L. Stein
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Stochastic Systems ◽  
Linear Time ◽  
The State ◽  
Optimal State ◽  
Unknown Inputs ◽  
Linear Time Invariant ◽  
Error Covariance ◽  
Time Invariant

Model-based machine diagnostics techniques require the modeled states and machine inputs to be measured. Because measurement of all the states and inputs is not always possible or practical, a simultaneous state and input observer is required. Previous work has developed this type of acausal observer and shown it is susceptible to noise. This paper develops a steady-state optimal observer that minimizes the trace of the steady-state error covariance of the state and input estimates for discrete, linear, time-invariant, stochastic systems with unknown inputs. In addition, a method to distinguish the best measurement set among the available measurement sets is developed. Results from numerical simulations show that the optimal observer can greatly improve estimation results in some cases.

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