Adaptive robustH∞state feedback control for linear uncertain systems with time-varying delay

This paper studies the problem of finite-time stabilization of a class of switched linear time-varying delay systems. An event-triggered sampling mechanism and an event-triggered state feedback control are proposed. Based on Lyapunov-like function method, linear matrix inequality technique and averaged dwell time method, sufficient conditions for switched delay systems under event-triggered state feedback control are given to ensure the finite-time stabilization of the switched delay systems. Finally, a numerical example is given to verify the validity of the proposed results.

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Variable structure observer design for a class of uncertain systems with a time-varying delay

International Journal of Applied Mathematics and Computer Science ◽

10.2478/v10006-012-0044-3 ◽

2012 ◽

Vol 22 (3) ◽

pp. 575-583 ◽

Cited By ~ 2

Author(s):

Wen-Jeng Liu

Keyword(s):

Uncertain Systems ◽

Sliding Mode ◽

Variable Structure ◽

Observer Design ◽

State Feedback Control ◽

Invariance Property ◽

Time Varying ◽

Time Varying Delay ◽

Error System ◽

Varying Delay

Abstract Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

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H∞Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

Mathematical Problems in Engineering ◽

10.1155/2015/473165 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

C. Emharuethai ◽

P. Niamsup

Keyword(s):

Nonlinear System ◽

State Feedback ◽

Sufficient Conditions ◽

State Feedback Control ◽

Linear Matrix ◽

Time Varying ◽

Matrix Inequalities ◽

Numerical Examples ◽

Time Varying Delay ◽

Varying Delay

H∞control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality.H∞controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theH∞state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

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Memory State Feedback Control for Time-Varying Delay Switched Fuzzy Systems

Advances in Fuzzy Systems ◽

10.1155/2019/4787925 ◽

2019 ◽

Vol 2019 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Le Zhang ◽

Meiyu Jia ◽

Hong Yang ◽

Gang Wu

Keyword(s):

Fuzzy Systems ◽

State Feedback ◽

Feedback Controller ◽

State Feedback Control ◽

Time Varying ◽

Memory State ◽

State Feedback Controller ◽

Time Varying Delay ◽

Memory State Feedback ◽

Varying Delay

Consider the problem of memoryless state feedback controller for time-delay system, which cannot consider both the memoryless and the memory items in the system. Therefore, the memoryless state feedback controller has certain limitations and is more conservative. This paper addresses the memory state feedback control for the time-varying delay switched fuzzy systems based on T-S fuzzy model to overcome the problem discussed above. The state vector and input of the time-varying delay systems contain unknown time-varying delay with known bounds. The designed controller whose parameters are solvable can introduce past state information and reduce the system conservativeness. The more general Lyapunov-Krasovskii functional is selected and the switching law is designed in order to analyze the open-loop system stability, and the memory state feedback controller is designed for the closed-loop system and the criterion for its asymptotic stability. Discuss the solvability of the above two criteria. Finally, a numerical example is given. The simulation results show that the proposed method is more feasible and effective.

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Refined Stability Conditions for Linear Uncertain Systems With Multiple Time-Varying Delays

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2397157 ◽

2006 ◽

Vol 129 (1) ◽

pp. 91-95 ◽

Cited By ~ 2

Author(s):

Chih-Peng Huang

Keyword(s):

Uncertain Systems ◽

State Feedback ◽

Multiple Time ◽

Time Varying ◽

Closed Loop System ◽

Stabilizing Controller ◽

Time Varying Delay ◽

The Stability ◽

Varying Delay ◽

Explicit Criteria

This paper mainly proposes distinct criteria for the stability analysis and stabilization of linear uncertain systems with time-varying delays. Based on the Lyapunov theorem, a sufficient condition of the unforced systems with single time-varying delay is first derived. By involving a memoryless state feedback controller, the condition will be extended to treat with the resulting closed-loop system. These explicit criteria can be reformulated in LMIs forms, so we will readily verify the stability or design a stabilizing controller by the current LMI solver. Furthermore, the considered systems with multiple time-varying delays are similarly addressed. Numerical examples are given to demonstrate that the proposed approach is effective and valid.

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