scholarly journals Simple Algebraic Criteria for Asymptotic Stability of a Class of TS Fuzzy Time-Delay Switched Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Nawel Aoun ◽  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Switched Systems ◽  
Type Systems ◽  
State Matrix ◽  
Comparison System ◽  
Switching Strategy ◽  
Fuzzy Models ◽  
Arbitrary Switching ◽  
Vector Norms

This paper investigates the asymptotic stability of a class of TS fuzzy switched systems when an arbitrary switching strategy is adopted. The proposed method, applied to neutral and retarded-type systems, is based on the vector-norms approach. The idea consists in defining a common comparison system to all the fuzzy models. If this comparison system can be described by a state matrix that fulfills the properties of the opposite of an M-matrix, then we can conclude on the asymptotic stability of the initial system via simple algebraic delay-independent conditions.

Observability and Distinguishability Properties and Stability of Arbitrarily Fast Switched Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Najah F. Jasim
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
External Disturbances ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Arbitrary Switching

This paper addresses sufficient conditions for asymptotic stability of classes of nonlinear switched systems with external disturbances and arbitrarily fast switching signals. It is shown that asymptotic stability of such systems can be guaranteed if each subsystem satisfies certain variants of observability or 0-distinguishability properties. In view of this result, further extensions of LaSalle stability theorem to nonlinear switched systems with arbitrary switching can be obtained based on these properties. Moreover, the main theorems of this paper provide useful tools for achieving asymptotic stability of dynamic systems undergoing Zeno switching.

Stability and controllability of switched systems

2013 ◽  
Vol 61 (3) ◽  
pp. 547-555 ◽  
Author(s):  
J. Klamka ◽  
A. Czornik ◽  
M. Niezabitowski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Arbitrary Switching ◽  
Mathematical Problems ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

scholarly journals Stabilization of Switched Time-Delay Linear Systems through a State-Dependent Switching Strategy

Actuators ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 261
Author(s):  
Tan Hou ◽  
Yuanlong Li ◽  
Zongli Lin
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Switched Systems ◽  
Optimization Problem ◽  
Small State ◽  
Restrictive Assumption ◽  
Delay Bound ◽  
Switching Strategy ◽  
State Delays ◽  
State Dependent

This paper considers the problem of stabilizing switched time-delay linear systems through a state-dependent switching strategy. In contrast to the existing works, we adopt a less restrictive assumption of the system, and show that this assumption is sufficient to guarantee asymptotic stability of the considered system under the min-projection switching strategy. Our results also imply that the min-projection switching strategy, originally designed for delay-free switched systems, is robust with respect to small state delays. An optimization problem is formulated to estimate the upper bound of the tolerable time delay. Numerical examples are presented to show that our method is applicable to a larger class of switched systems and leads to a greater delay bound.

Adaptive event-triggered control for master-slave switched systems subject to attacked state-dependent switching law

2021 ◽  
pp. 014233122098594
Author(s):  
Lingcong Nie ◽  
Xindi Xu ◽  
Yan Li ◽  
Weiyu Jiang ◽  
Yiwen Qi ◽  
...  
Keyword(s):  
Time Delay ◽  
Switched Systems ◽  
System Performance ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Switched System ◽  
Switching Law ◽  
Variable Threshold ◽  
Event Triggering ◽  
Event Triggered

This paper investigates adaptive event-triggered [Formula: see text] control for network-based master-slave switched systems subject to actuator saturation and data injection attacks. It is an important and unrecognised issue that the switching signal is affected from both event-triggering scheme and network attacks. An adaptive event-triggering scheme is proposed that can adjust the triggering frequency through a variable threshold based on system performance. Furthermore, considering the impacts of transmission delays and actuator saturation, an event-triggered time-delay error switched system is developed. Subsequently, by utilizing piecewise Lyapunov functional technique, sufficient conditions are derived to render the time-delay error switched system to have an [Formula: see text] performance level. In particular, the coupling between switching instants and data updating instants is analyzed during the system performance analysis. Moreover, sufficient conditions for the desired state-feedback controller gains and event-triggering parameter are presented. Finally, a numerical example is given to verify the effectiveness of the proposed method.

scholarly journals Optimal control of switched systems with time delay

2006 ◽  
Vol 19 (10) ◽  
pp. 1062-1067 ◽  
Author(s):  
Changzhi Wu ◽  
Kok Lay Teo ◽  
Rui Li ◽  
Yi Zhao
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Switched Systems

scholarly journals Overlapping Decentralized Controller Design for Descriptor-type Systems with Distributed Time-delay

2021 ◽  
Vol 20 ◽  
pp. 257-263
Author(s):  
Altug Iftar
Keyword(s):  
Time Delay ◽  
Large Scale ◽  
Controller Design ◽  
Original System ◽  
Type Systems ◽  
Large Scale System ◽  
Decentralized Controllers ◽  
Distributed Time Delay

Decentralized controller design using overlapping decompositions is considered for descriptor-type systems with distributed time-delay. The approach is based on the principle of extension. In this approach, a given large-scale system is decomposed overlappingly into a number of subsystems and expanded such that the overlapping parts appear as disjoint. A decentralized controller is then designed for the expanded system. This controller is then contracted for implementation on the original system. It is shown that if the decentralized controllers are designed to stabilize the expanded system and to achieve certain performance, then the contracted controller, which would have an overlapping decentralized structure, will stabilize the original system and will achieve corresponding performance

scholarly journals Controller Design for Descriptor-type Systems with Distributed Timedelay Using Extension

2021 ◽  
Vol 20 ◽  
pp. 27-32
Author(s):  
Altug Iftar
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Original System ◽  
Type Systems ◽  
Distributed Time Delay

Controller design using extension is considered for descriptor-type systems with distributed time-delay. The approach is useful in decentralized controller design using overlapping decompositions. In this approach, a given largescale system is decomposed overlappingly into a number of subsystems and expanded such that the overlapping parts appear as disjoint. Since the subsystems appear as disjoint for the expanded system, it is easier to design a descentralized controller for the expanded system. This controller is then contracted for implementation on the original system. In the present paper, it is shown how to contract such a controller to guarantee stability and desired performance for the original system

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