A necessary and sufficient condition for robust asymptotic stability of time-variant discrete systems

Bauer, Péter; Premaratne, Kamal; Duran, J. Peter

doi:10.1109/9.237661

Cited by 78 publications

(48 citation statements)

References 9 publications

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“…(9) represents the dynamics of a linear time-varying system. We use the results in [16] to derive convergence conditions on the time-varying matrices K(t) and λ(t). A necessary and sufficient condition for global asymptotic stability is given in [16], by which there exists a finite k > 0 such that…”

Section: Convergence Analysismentioning

confidence: 99%

A distributed pareto-optimal dynamic estimation method

Boem

Fischione

et al. 2015

2015 European Control Conference (ECC)

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Abstract-In this paper, a novel distributed model-based prediction method is proposed using sensor networks. Each sensor communicates with the neighboring nodes for state estimation based on a consensus protocol without centralized coordination. The proposed distributed estimator consists of a consensus-filtering scheme, which uses a weighted combination of sensors information, and a model-based predictor. Both the consensus-filtering weights and the model-based prediction parameter for all the state components are jointly optimized to minimize the variance and bias of the prediction error in a Pareto framework. It is assumed that the weights of the consensus-filtering phase are unequal for the different state components, unlike consensus-based approaches from literature. The state, the measurements, and the noise components are assumed to be individually correlated, but no probability distribution knowledge is assumed for the noise variables. The optimal weights are derived and it is established that the consensus-filtering weights and the model-based prediction parameters cannot be designed separately in an optimal way. The asymptotic convergence of the mean of the prediction error is demonstrated. Simulation results show the performance of the proposed method, obtaining better results than distributed Kalman filtering.

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Section: Convergence Analysismentioning

confidence: 99%

A distributed pareto-optimal dynamic estimation method

Boem

Fischione

et al. 2015

2015 European Control Conference (ECC)

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“…For such purpose, let us first introduce a technical lemma [2] for the robust stability of linear time variant systems…”

Section: Stability Analysismentioning

confidence: 99%

Persistent disturbance attenuation properties for networked control systems

Lin

Antsaklis

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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Abstract-In this paper, both the asymptotic stability and l ∞ persistent disturbance attenuation issues are investigated for a class of Networked Control Systems (NCSs) under bounded uncertain access delay and packet dropout effects. The basic idea is to formulate such NCSs as discrete-time switched systems with arbitrary switchings. Then the NCSs' stability and performance problems can be reduced to the corresponding problems of such switched systems. The asymptotic stability problem is considered first, and a necessary and sufficient condition is derived for the NCSs' asymptotic stability based on robust stability techniques. Secondly, the NCSs' l ∞ persistent disturbance attenuation properties are studied, and an algorithm is proposed to calculate the l ∞ induced gain of the NCSs. The decidability issue of the algorithm is also discussed.

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“…To the best of our knowledge, the work of Bauer et al [10], along with [16][17][18], gives the tightest stability conditions for parametric uncertainties of type…”

Section: Robust Stability Of Time-varying Linear Systemsmentioning

confidence: 99%

“…The design problem on non-uniform discrete-time domains can be successfully approached by exploiting interesting results on robust stability (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]) for perturbed systems of type…”

Section: Robust Stability Of Time-varying Linear Systemsmentioning

confidence: 99%

Controller Synthesis on Non-uniform and Uncertain Discrete–Time Domains

Balluchi¹,

Murrieri²,

Sangiovanni‐Vincentelli

2005

Hybrid Systems: Computation and Control

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Abstract. The problem of synthesizing feedback controllers that perform sensing and actuation actions on non-uniform and uncertain discrete time domains is considered. This class of problems is relevant to many application domains. For instance, in engine control a heterogenous and, to some extent, uncertain event-driven time domain is due to the behavior of the 4-stroke internal combustion engine, with which the controller has to synchronize to operate properly. Similar problems arise also in standard discrete-time control systems when considering the behavior of the system with controller implementation and communication effects. The design problem is formalized in a hybrid system framework; synthesis and verification methods, based on robust stability and robust performance results, are presented. The effectiveness of the proposed methods is demonstrated in an engine control application.

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A necessary and sufficient condition for robust asymptotic stability of time-variant discrete systems

Cited by 78 publications

References 9 publications

A distributed pareto-optimal dynamic estimation method

A distributed pareto-optimal dynamic estimation method

Persistent disturbance attenuation properties for networked control systems

Controller Synthesis on Non-uniform and Uncertain Discrete–Time Domains

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