Constructive Necessary and Sufficient Condition for the Stability of Quasi-Periodic Linear Impulsive Systems

Fiacchini, Mirko; Morărescu, Irinel-Constantin

doi:10.1109/tac.2015.2496792

Cited by 17 publications

(26 citation statements)

References 16 publications

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“…Proof: The proof consists in demonstrating that (24) and (25) are equivalent. An analogous result has been proved in [6].…”

Section: Stability Analysis: Necessary and Sufficient Conditionssupporting

confidence: 73%

“…x = (x p , w, x k , v) with n = n p + m + n k + p, and A c , A 1 and A 2 are appropriate matrices defined from (4)- (6). Dynamics (7) can be also obtained in the framework of multi-agent systems that update asynchronously their inputs.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The overall system is exponentially stable in closed loop. The matrices A c , A 1 and A 2 in (7) are obtained by using the numerical values given above in equations (4)- (6). We consider the asynchronous sampling times T 1 = 3a and T 2 = 7a and try to maximize a such that the resulting sampled-data system is exponentially stable for every possible initialization of the clocks.…”

Section: Numerical Examplementioning

confidence: 99%

“…Stability and stabilization of linear impulsive systems with quasi-periodic impulsions have been considered in [11]. Furthermore, we proposed in [6] a constructive methodology to get necessary and sufficient conditions for the stability of this class of systems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability analysis for systems with asynchronous sensors and actuators

Fiacchini¹,

Morărescu²

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-The paper provides computation-oriented necessary and sufficient conditions for the global exponential stability of linear systems with asynchronous sensors and actuators. Precisely, we focus on continuous-time linear systems whose state undergoes finite jumps referred to as impulsions. The impulsions are of two types: those related to input updates and those related to measurement updates. We assume that impulsions of each type occur periodically but the periods may be different and the clocks at the sensor and at the actuator are not synchronized. We first show that the analysis can be reduced to a finite time domain. Based on that, we provide necessary and sufficient conditions for the global exponential stability of systems belonging to the class under study. An example illustrates numerically the proposed results.

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“…Proof: The proof consists in demonstrating that (24) and (25) are equivalent. An analogous result has been proved in [6].…”

Section: Stability Analysis: Necessary and Sufficient Conditionssupporting

confidence: 73%

Section: Problem Formulationmentioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability analysis for systems with asynchronous sensors and actuators

Fiacchini¹,

Morărescu²

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

Self Cite

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show abstract

“…A mixed continuous and discrete-time approach has been proposed in [16], [17] through the concept of looped-functionals and adapted to the case of impulsive systems in [18]. In [19] polyhedral Lyapunov functions are employed to obtain necessary and sufficient stability conditions and a constructive method for testing the stability. Finally, [20] deals with the stability verification problem using reachability analysis.…”

Section: Introductionmentioning

confidence: 99%

Stability of Sampled-Data Control Systems Under Aperiodic Sampling and Input Saturation

Fiacchini¹,

Silva²

2018

2018 IEEE Conference on Decision and Control (CDC)

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This work proposes a new approach to asses stability of sampled-data controlled linear systems under aperiodic sampling and subject to input saturation. From an impulsive representation of the system and considering a partition of the interval between two successive sampling instants, it is shown that the discrete-time dynamics of the closed-loop system can be described by a difference inclusion. A general Lyapunovbased result allowing to conclude about the local stability of the sampled-data system is derived. Thus, considering the particular case of quadratic functions, a constructive condition in terms of linear matrix inequalities (LMIs) is proposed to compute estimates of the region of attraction of the nonlinear closed-loop system.

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Dwell‐time‐dependent conditions for exponential stability and hybrid L₂ × l₂‐gain of linear neutral time‐delay systems with impulsive effects

Chen

Lü

2021

Intl J Robust & Nonlinear

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This article considers the problems of achieving exponential stability and finite hybrid L 2 × l 2 -gain with respect to continuous and discrete disturbances for linear neutral time-delay systems with impulsive effects. In the framework of descriptor system representation, a piecewise timer-dependent Lyapunov functional is introduced to analyze the double impacts of state-delay and impulse-dwell-time on stability of the underlying system. This functional depends on the state over an impulse interval and the state over a delay interval. Its construction is based on a delay-fractioning scheme which ensures all delay subintervals contains at most one impulse instant. The relations among the augmented state variables are explored by using the impulse-timer functions and the Newton-Leibniz formula. It is proved that the positive definiteness property of the functional at nonimpulse instants is not necessary for ensuring stability. The hybrid L 2 × l 2 -gain analysis is carried out by jointly using the introduced functional and a discrete-time Lyapunov function. The obtain criteria for exponential stability and hybrid L 2 × l 2 -gain are expressed in terms of linear matrix inequalities. Their effectiveness is verified through two numerical examples. K E Y W O R D Sdelay fractioning, exponential stability, hybrid L 2 × l 2 -gain, impulse-timer-dependent Lyapunov functional, neutral time-delay systems with impulsive effects 4782

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Constructive Necessary and Sufficient Condition for the Stability of Quasi-Periodic Linear Impulsive Systems

Cited by 17 publications

References 16 publications

Stability analysis for systems with asynchronous sensors and actuators

Stability analysis for systems with asynchronous sensors and actuators

Stability of Sampled-Data Control Systems Under Aperiodic Sampling and Input Saturation

Dwell‐time‐dependent conditions for exponential stability and hybrid L₂ × l₂‐gain of linear neutral time‐delay systems with impulsive effects

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Constructive Necessary and Sufficient Condition for the Stability of Quasi-Periodic Linear Impulsive Systems

Cited by 17 publications

References 16 publications

Stability analysis for systems with asynchronous sensors and actuators

Stability analysis for systems with asynchronous sensors and actuators

Stability of Sampled-Data Control Systems Under Aperiodic Sampling and Input Saturation

Dwell‐time‐dependent conditions for exponential stability and hybrid L2 × l2‐gain of linear neutral time‐delay systems with impulsive effects

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Product

Resources

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Dwell‐time‐dependent conditions for exponential stability and hybrid L₂ × l₂‐gain of linear neutral time‐delay systems with impulsive effects