The Stability Analysis and Controllers Design with Packet Dropouts for Discrete-Time NCSs Based on Augmented Switched System

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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A delay-partitioning approach to the stability analysis of discrete-time systems

Automatica ◽

10.1016/j.automatica.2009.12.004 ◽

2010 ◽

Vol 46 (3) ◽

pp. 610-614 ◽

Cited By ~ 163

Author(s):

Xiangyu Meng ◽

James Lam ◽

Baozhu Du ◽

Huijun Gao

Keyword(s):

Stability Analysis ◽

Discrete Time ◽

Discrete Time Systems ◽

The Stability ◽

Time Systems ◽

Delay Partitioning

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Delay-dependent stability analysis for discrete-time switched linear systems with parametric uncertainties

Journal of Vibration and Control ◽

10.1177/1077546317739735 ◽

2017 ◽

Vol 24 (20) ◽

pp. 4921-4930 ◽

Cited By ~ 12

Author(s):

Nasrollah Azam Baleghi ◽

Mohammad Hossein Shafiei

Keyword(s):

Stability Analysis ◽

Time Delay ◽

Discrete Time ◽

Upper Bound ◽

Sufficient Conditions ◽

Switched System ◽

Parametric Uncertainties ◽

Time Varying ◽

Delay Dependent ◽

Delay Dependent Stability

This paper studies the delay-dependent stability conditions for time-delay discrete-time switched systems. In the considered switched system, there are uncertain terms in each subsystem due to affine parametric uncertainties. Additionally, each subsystem has a time-varying state delay which adds more complexity to the stability analysis. Based on the Lyapunov functional approach, the sufficient conditions are extracted to determine the admissible upper bound of the time-varying delay for guaranteed stability. Furthermore, a class of switching signals is identified to guarantee the exponential stability of the uncertain time-delay switched system. The main advantage of the suggested switching signals is its independency to the uncertainties. Furthermore, these signals are only constrained by a determined average dwell time (may be chosen arbitrarily). Finally, a numerical example is provided to demonstrate the efficiency of the proposed method and also the reduction of conservatism in finding the admissible upper bound of time-delay in comparison with other stability analysis approaches.

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Modeling and Stability Analysis of Dynamic Control Through a Soft Interface

Journal of Robotics and Mechatronics ◽

10.20965/jrm.2006.p0242 ◽

2006 ◽

Vol 18 (3) ◽

pp. 242-248 ◽

Cited By ~ 2

Author(s):

Mizuho Shibata ◽

◽

Shinichi Hirai

Keyword(s):

Stability Analysis ◽

Discrete Time ◽

Feedforward Control ◽

Dynamic Control ◽

System Stability ◽

Critical Stability ◽

Runge Kutta Method ◽

The Stability ◽

The Relationship ◽

Soft Interface

To analyze the stability of dynamic control through asoft interface-the viscoelastic material between a manipulating finger and a manipulated object- we model dynamic control through the soft interface in continuous-discrete time. We then formulate dynamics using a modified z-transform in continuous-discrete time for feedback and feedforward control. We show that system stability depends on the viscoelasticity of the soft interface for feedback control. The relationship between material viscosity and sampling time in critical stability is not monotonous, a phenomenon we analyze by root locus. We compare stability analysis by the modified z-transform, simulations based on the Runge-Kutta method, and a regular z-transform, demonstrating that the relationship is specific to a continuous-discrete time.

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Switching Control Design for Switched Fuzzy Discrete-Time Systems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1006-1007.711 ◽

2014 ◽

Vol 1006-1007 ◽

pp. 711-714

Author(s):

Hong Yang ◽

Huan Huan Lü ◽

Le Zhang

Keyword(s):

Stability Analysis ◽

Discrete Time ◽

Fuzzy Systems ◽

Closed Loop ◽

Control Method ◽

Control Design ◽

Switching Control ◽

Discrete Time Systems ◽

The Stability ◽

Time Systems

This paper investigates the problems of stability analysis and stabilization for a class of switched fuzzy discrete-time systems. Based on a common Lyapunov functional, a switching control method has been developed for the stability analysis of switched discrete-time fuzzy systems. A new stabilization approach based on a switching parallel distributed compensation scheme is given for the closed-loop switched fuzzy systems. Finally, the illustrative example is provided to demonstrate the effectiveness of the techniques proposed in this paper.

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Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.341-342.668 ◽

2013 ◽

Vol 341-342 ◽

pp. 668-673

Author(s):

Yi Min Li ◽

Yuan Yuan Li

Keyword(s):

Stability Analysis ◽

Discrete Time ◽

Fuzzy Model ◽

Optimization Techniques ◽

Linear Matrix ◽

Time Varying ◽

Parameter Uncertainties ◽

Lmi Optimization ◽

System A ◽

The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

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Entwurf von zeitkontinuierlichen ΣΔ-Modulatoren – Äquivalenz zwischen zeitkontinuierlichen und zeitdiskreten Systemen

Advances in Radio Science ◽

10.5194/ars-5-221-2007 ◽

2007 ◽

Vol 5 ◽

pp. 221-224

Author(s):

J. Anders ◽

W. Mathis ◽

M. Ortmanns

Keyword(s):

Stability Analysis ◽

Discrete Time ◽

Input Signal ◽

Continuous Time ◽

Wird Eine ◽

Loop Delay ◽

Discrete Time Systems ◽

Excess Loop Delay ◽

The Stability ◽

Time Systems

Abstract. Im vorliegenden Artikel wird eine vollstängige, d.h. unter Einbeziehung des Eingangssignals, Äquivalenz zwischen zeitkontinuierlichen und zeitdiskreten ΣΔ-Modulatoren im Zustandsraum hergeleitet. Es wird ebenfalls gezeigt, wie eine wichtige Nichtidealität, das sog. "excess loop delay", in den Berechnungen berücksichtigt werden kann. Die dargestellte Methode dient dazu, den Entwurf und dabei vor allem die Stabilitätsuntersuchungen, von zeitkontinuierlichen ΣΔs auf die bereits empirisch intensiv erforschten zeitdiskreten Systeme zurückzuführen. In the article at hand a complete equivalency, i.e. including the input signal, between continuous-time and discrete-time ΣΔ-modulators in state-space is derived. In addition, it is shown, how one can incorporate the important non-ideality of "excess loop delay" into the formalism. The method introduced is supposed to facilitate the design, especially the stability analysis part of the design, of continuous-time ΣΔs by making use of the empirically thoroughly examined discrete-time systems.

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Stability analysis of an eco-epidemiological model incorporating a prey refuge

Nonlinear Analysis Modelling and Control ◽

10.15388/na.15.4.14319 ◽

2010 ◽

Vol 15 (4) ◽

pp. 473-491 ◽

Cited By ~ 13

Author(s):

A. K. Pal ◽

G. P. Samanta

Keyword(s):

Stability Analysis ◽

Time Delay ◽

Computer Simulations ◽

Discrete Time ◽

Predator Population ◽

Prey Refuge ◽

Predator Prey ◽

Predator Prey Model ◽

Discrete Time Delay ◽

The Stability

The present paper deals with the problem of a predator-prey model incorporating a prey refuge with disease in the prey-population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours such as boundedness, permanence, local and global stabilities are addressed. We have also studied the effect of discrete time delay on the model. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings.

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