scholarly journals Finite-time stability of discrete-time systems with time-varying delay

2012 ◽  
Vol 18 (4-1) ◽  
pp. 525-533 ◽  
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic ◽  
Nebojsa Dimitrijevic
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Original System ◽  
Delay Systems ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Maximum Delay ◽  
Varying Delay

Finite-time stability can be used in all applications where large values of the state are not acceptable. In this paper, finite-time stability problem for a class of linear time-varying delay systems is studied. Based on Lyapunov-like functions method and using an appropriate model transformation of the original system, the sufficient delay-dependent finite-time stability conditions are derived. The criteria are presented in the form of LMIs, which are dependent on the minimum and maximum delay bounds. The numerical examples are presented to illustrate the applicability of the developed results.

scholarly journals Finite-Time Stability and Stabilization of Switched Linear Time-Varying Systems with Time-Varying Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lulu Feng ◽  
Ping Zhao
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Average Dwell Time ◽  
Control Input ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Time Varying Systems ◽  
Varying Delay

This paper deals with the finite-time stability (FTS) of switched linear time-varying (SLTV) systems with time-varying delay. Firstly, based on Lyapunov–Krasovskii functional technique and average dwell time (ADT) approach, a sufficient criterion on FTS for SLTV systems with time-varying delay is obtained. For the SLTV system with delay and control input, based on the criterion, a state feedback controller is designed such that the closed-loop system is finite-time stable (FTS). Finally, an example is employed to illustrate the validity of our results.

scholarly journals Finite-Time Stability of Uncertain Nonlinear Systems with Time-Varying Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jingting Hu ◽  
Guixia Sui ◽  
Shengli Du ◽  
Xiaodi Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Delay Systems ◽  
Time Varying ◽  
Uncertain Nonlinear Systems ◽  
Time Stability ◽  
External Disturbances ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Varying Delay

The problem of finite-time stability for a class of uncertain nonlinear systems with time-varying delay and external disturbances is investigated. By using the Lyapunov stability theory, sufficient conditions for the existence of finite-time state feedback controller for this class of systems are derived. The results can be applied to finite-time stability problems of linear time-delay systems with parameter uncertainties and external disturbances. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.

scholarly journals New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten B. Stojanovic
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Maximum Delay ◽  
Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.

scholarly journals NEW RESULTS ON FINITE-TIME STABILITY FOR NONLINEAR FRACTIONAL ORDER LARGE SCALE SYSTEMS WITH TIME VARYING DELAY AND INTERCONNECTIONS

2020 ◽  
Vol 225 (02) ◽  
pp. 52-57
Author(s):  
Phạm Ngọc Anh ◽  
Nguyễn Trường Thanh ◽  
Hoàng Ngọc Tùng
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Large Scale ◽  
Time Varying ◽  
Time Stability ◽  
Large Scale Systems ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Varying Delay

Bài báo này khảo sát tính ổn định hữu hạn của một lớp hệ quy mô lớn cấp phân số có trễ biến thiên và nhiễu phi tuyến. Sử dụng bất đẳng thức Gronwall tổng quát, một điều kiện đủ cho ổn định hữu hạn của các hệ này được thiết lập thông qua hàm Mittag-Leffler. Kết quả thu được sau đó được áp dụng cho hệ bất định và hệ không ôtonom có trễ biến thiên và nhiễu phi tuyến.

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