Search results for "Exponential stability"

showing 4 items of 84 documents

On the qualitative analysis of the solutions of a mathematical model of social dynamics

2006

Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.

education.field_of_studyPopulation modelsDynamical systems theoryDiscretizationAsymptotic stabilityApplied MathematicsStochastic gamePopulationComplex systemBoltzmann modelsDynamical systemSocial dynamicsExponential stabilityApplied mathematicseducationKinetic theoryMathematical economicsNonlinearityMathematicsDiscretizationApplied Mathematics Letters
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Positive L1 observer design for positive Switched systems

2014

Published version of an article in the journal: Circuits, Systems, and Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1007/s00034-013-9737-6 This paper investigates the problem of L1 observer design for positive switched systems. Firstly, a new kind of positive L1 observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive L1 observer. Under the condition obtained, the estimated error converges to zero exponentially, and the L1 -gain from the disturbance input to the estimated error is less t…

exponetial stabiblityApplied MathematicsSignal ProcessingVDP::Technology: 500::Mechanical engineering: 570positive observerswitched systemstime-varying delaysAverage dwell time; Exponential stability; Positive observer; Switched systems; Time-varying delays; Signal Processing; Applied MathematicsExponential stabilityVDP::Mathematics and natural science: 400::Mathematics: 410::Analysis: 411average dwell time
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Stability of stochastic nonlinear systems with state-dependent switching

2013

In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô’s formula and Dynkin’s formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-…

stochastic systemsStability (learning theory)Mathematical proofnonlinear control systemsSet (abstract data type)State-dependent switching; Stochastic systems; Switched systems; Control and Systems Engineering; Computer Science Applications1707 Computer Vision and Pattern Recognition; Electrical and Electronic EngineeringExponential stabilityControl theoryElectrical and Electronic EngineeringSwitched systemsMathematicsLyapunov methodsStochastic systemsSeries (mathematics)Stochastic processApplied MathematicsComputer Science Applications1707 Computer Vision and Pattern Recognitionstate-dependent switchingstabilityComputer Science ApplicationsNonlinear systemControl and Systems EngineeringState dependentswitched systemscontrol system synthesisState-dependent switching
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Robust H<inf>∞</inf> control of Markovian jump systems with mixed time delays

2010

In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H ∞ control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H ∞ performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results i…

symbols.namesakeExponential stabilityControl theoryRobustness (computer science)Linear systemsymbolsMarkov processState (functional analysis)Robust controlStability (probability)Mathematics49th IEEE Conference on Decision and Control (CDC)
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