Pinning Synchronization of Directed Networks With Switching Topologies: A Multiple Lyapunov Functions Approach

Abstract Experimental and anecdotal evidences have shown that state-switched control strategies for piezoelectric actuators can be advantageous. However, most discussions of the stability of these systems has relied on heuristic, or physically motivated, arguments. In this paper, we show that recent open-circuit/short-circuit state-switching control laws can be viewed as hybrid dynamical systems of Witsenhausen type. Within this framework, the closed-loop stability of OC/SC switching is rigorously established using the method of multiple Lyapunov functions.

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Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2238874 ◽

2005 ◽

Vol 128 (3) ◽

pp. 696-700 ◽

Cited By ~ 43

Author(s):

Zhijian Ji ◽

Xiaoxia Guo ◽

Long Wang ◽

Guangming Xie

Keyword(s):

Linear Systems ◽

Lyapunov Functions ◽

State Feedback ◽

Robust Stabilization ◽

Disturbance Attenuation ◽

Control Synthesis ◽

Linear Matrix ◽

Multiple Lyapunov Functions ◽

Switched Linear Systems ◽

Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

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Anti-swing control of underactuated overhead crane system using multiple Lyapunov functions

2011 IEEE International Conference on Mechatronics and Automation ◽

10.1109/icma.2011.5985696 ◽

2011 ◽

Cited By ~ 1

Author(s):

Aydin Yesildirek

Keyword(s):

Lyapunov Functions ◽

Overhead Crane ◽

Multiple Lyapunov Functions

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Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

Mathematical Problems in Engineering ◽

10.1155/2015/502475 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 5

Author(s):

V. Nosov ◽

J. A. Meda-Campaña ◽

J. C. Gomez-Mancilla ◽

J. O. Escobedo-Alva ◽

R. G. Hernández-García

Keyword(s):

Stability Analysis ◽

Finite Number ◽

Switched Systems ◽

Lyapunov Functions ◽

Switched System ◽

Linear Functions ◽

Asymptotically Stable ◽

Multiple Lyapunov Functions ◽

Stability Theorems ◽

The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

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Exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331218757859 ◽

2018 ◽

Vol 41 (2) ◽

pp. 350-365 ◽

Cited By ~ 1

Author(s):

Xin Zhang ◽

Huashan Liu ◽

Yiyuan Zheng ◽

Yuqing Sun ◽

Wuneng Zhou ◽

...

Keyword(s):

Exponential Stability ◽

Lyapunov Functions ◽

Stochastic Systems ◽

Transition Probabilities ◽

Time Varying ◽

Analysis Method ◽

Multiple Lyapunov Functions ◽

Time Varying Delay ◽

Neutral Stochastic Systems ◽

Varying Delay

This paper discusses the problem of exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay. Based on non-convolution type multiple Lyapunov functions and stochastic analysis method, we obtain the conditions which are independent to any decay rate of the exponential stability for uncertain transition probabilities neutral stochastic systems with time-varying delay. Finally, two examples are presented to illustrate the effectiveness and potential of the proposed results.

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