Exponential stability analysis for 2D discrete switched systems with state delays

2019 ◽  
Vol 40 (6) ◽  
pp. 1088-1103 ◽  
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Zakaria Chalh
Keyword(s):  
Stability Analysis ◽  
Exponential Stability ◽  
Switched Systems ◽  
State Delays ◽  
Discrete Switched Systems

scholarly journals Delay-Dependent Stability Analysis for Uncertain Switched Time-Delay Systems Using Average Dwell Time

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yangming Zhang ◽  
Peng Yan
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Exponential Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Delay Dependent

We are concerned with the stability problem for linear discrete-time switched systems with time delays. The problem is solved by using multiple Lyapunov functions to develop constructive tools for the exponential stability analysis of the switched time-delay system. Furthermore, the uncertainties of the switched systems are also taken into consideration. Sufficient delay-dependent conditions are derived in terms of the average dwell time for the exponential stability based on linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Varying Motor Assistance During Biceps Curls Induced via Functional Electrical Stimulation

2018 ◽  
Author(s):  
Courtney A. Rouse ◽  
Christian A. Cousin ◽  
Victor H. Duenas ◽  
Warren E. Dixon
Keyword(s):  
Electrical Stimulation ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Functional Electrical Stimulation ◽  
Switched Systems ◽  
Biceps Brachii ◽  
Robot Assisted ◽  
Robot System ◽  
Rehabilitation Protocols ◽  
And Performance

Robot-assisted therapy has been established as a useful rehabilitation tool for motor recovery in people with various neurological impairments; however, balancing human and robot contribution, such that the target muscle is sufficiently exercised, is necessary to improve the outcome of rehabilitation protocols. Functional Electrical Stimulation (FES) can assist a person to move their limb by contracting the muscle; however, motor assistance is often necessary to accurately follow a desired limb trajectory, especially since stimulation can be limited due to various factors (e.g., subject comfort, stimulation saturation). In this paper, a motor is tasked with intermittently assisting the FES-activated biceps brachii in tracking a desired forearm trajectory whenever the FES input reaches a pre-set comfort threshold. A Lyapunov-like switched systems stability analysis is used to prove exponential stability of the human-robot system. Preliminary experiments demonstrate the feasibility and performance of the controller on two subjects with neurological impairments.

scholarly journals Stabilization and Controller Design of 2D Discrete Switched Systems with State Delays under Asynchronous Switching

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Shipei Huang ◽  
Zhengrong Xiang ◽  
Hamid Reza Karimi
Keyword(s):  
Switched Systems ◽  
Dwell Time ◽  
State Feedback ◽  
Controller Design ◽  
Robust Stabilization ◽  
Asynchronous Switching ◽  
Parameter Uncertainties ◽  
State Delays ◽  
Discrete Switched Systems ◽  
The Stability

This paper is concerned with the problem of robust stabilization for a class of uncertain two-dimensional (2D) discrete switched systems with state delays under asynchronous switching. The asynchronous switching here means that the switching instants of the controller experience delays with respect to those of the system. The parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee the exponential stability. The dwell time approach is utilized for the stability analysis and controller design. A numerical example is given to illustrate the effectiveness of the proposed method.

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