A Recursive Algorithm by using Eigenvector Method for Identifying Multivariable Linear Time-Invariant Systems

1982 ◽  
Author(s):  
Yuan Tian-Xing ◽  
Li Duan ◽  
Zhang Zhong-Jun
Keyword(s):  
Linear Time ◽  
Recursive Algorithm ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

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.

Zeno-free adaptive event-triggered control design

2018 ◽  
Vol 41 (8) ◽  
pp. 2328-2337 ◽  
Author(s):  
Hassan Adloo ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Performance Criterion ◽  
Linear Time Invariant ◽  
Event Triggering ◽  
Linear Time Invariant Systems ◽  
System States ◽  
Time Invariant ◽  
Event Triggered

This paper presents a new general framework for adaptive event-triggered control strategy to extend average inter-event interval, while maintaining the performance of the system. The proposed event-triggering mechanism is acquired from input to state stability conditions, which is defined in terms of system states as well as an adaptation parameter. Under the Lipschitz assumption, a positive lower bound on sampling durations is also established that is essential to restrain the Zeno behavior. Applying the proposed method to linear time-invariant systems, leads to sufficient conditions to guarantee asymptotic stability in the form of matrix inequalities. Moreover, it is shown that there exist more degrees of freedom to improve the performance criterion from theoretical aspects. Finally, in order to show capability of the proposed method and its better performance compared with some recent works, numerical simulations are presented.

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