Controllability and adaptation of linear time-invariant systems under irregular and Markovian sampling

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.

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Robust Stabilization of Linear Time-Invariant Systems Via Linear Control

Robustness in Identification and Control ◽

10.1007/978-1-4615-9552-6_22 ◽

1989 ◽

pp. 311-319 ◽

Cited By ~ 1

Author(s):

Kehui Wei

Keyword(s):

Linear Time ◽

Robust Stabilization ◽

Linear Control ◽

Linear Time Invariant ◽

Linear Time Invariant Systems ◽

Time Invariant

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Zeno-free adaptive event-triggered control design

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331218799147 ◽

2018 ◽

Vol 41 (8) ◽

pp. 2328-2337 ◽

Cited By ~ 5

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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