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Linear ultimate boundedness control of uncertain dynamical systems
Automatica, 1983Given a state equation whose description includes uncertain parameters, it is often desirable to design a feedback controller which renders all solutions uniformly and ultimately bounded. When facing such a problem, one often has available or assumes an upper bound for the excursions of the uncertain parameters.
Ian Petersen +2 more
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Ultimate boundedness of impulsive fractional delay differential equations
Applied Mathematics Letters, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liguang Xu
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Exponential ultimate boundedness of impulsive stochastic delay differential equations
Applied Mathematics Letters, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liguang Xu, Danhua He
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2015
Physically-motivated systems are generally subject to nonlinearities and uncertainties; for these systems, classical stability definitions (like asymptotic or exponential stability in the sense of Lyapunov) can be too restrictive. Namely, the state of a system may be mathematically unstable in some classical sense, but the response oscillates close ...
Martha Belem Saldivar Márquez +3 more
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Physically-motivated systems are generally subject to nonlinearities and uncertainties; for these systems, classical stability definitions (like asymptotic or exponential stability in the sense of Lyapunov) can be too restrictive. Namely, the state of a system may be mathematically unstable in some classical sense, but the response oscillates close ...
Martha Belem Saldivar Márquez +3 more
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Ultimate boundedness conditions for a hybrid model of population dynamics
21st Mediterranean Conference on Control and Automation, 2013This paper addresses the ultimate boundedness and permanence analysis for a Lotka-Volterra type system with switching of parameter values. Two new approaches for the constructing of common Lyapunov function for the family of subsystems corresponding to the switched system are suggested. Sufficient conditions in terms of linear inequalities are obtained
Alexander Yu. Aleksandrov +2 more
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Ultimate boundedness for nonautonomous diffusive Lotka-Volterra patches
Mathematical Biosciences, 1988The asymptotic behavior of n biological species living in two patches is investigated. The governing mathematical model reads as a system of ordinary differential equations of the form \[ \dot x_ i=x_ i[e_ x(t)+A_ x(t)x]_ i+D_ i(t)(y_ i-x_ i),\quad \dot y_ i=y_ i[e_ y(t)+A_ y(t)y]_ i+D_ i(t)(x_ i-y_ i), \] i\(=1,2,...,n\), where \(e_ x,e_ y: {\mathbb{R}
BERETTA E +2 more
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Ultimate Boundedness and Invariant Measure
2011We study ultimate boundedness in the m.s.s. of solutions to SDE’s, namely the following property, \(E\| X^{x}(t)\|^{2}_{H}\leq c\mathrm{e}^{-\beta t}\| x\|_{H}^{2}+M\), \(c,\; \beta >0 ...
Leszek Gawarecki, Vidyadhar Mandrekar
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Almost dissipativity and ultimate boundedness property for switched nonlinear systems
International Journal of Control, 2021This paper establishes almost dissipativity theory for switched nonlinear systems. First, an almost dissipativity of switched nonlinear systems is defined using multiple storage functions and multi...
Hongbo Pang, Shuo Liu 0013
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Uniform ultimate boundedness of nonlinear nonstationary systems
Vestnik St. Petersburg University: Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aleksandrov, A. Yu., Zhabko, A. P.
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Exponential ultimate boundedness and stability of stochastic differential equations with impulese
Asian Journal of Control, 2022AbstractThe paper mainly studies globally pth moment exponentially ultimate boundedness and pth moment exponential stability of impulsive stochastic functional differential equations. By using the Lyapunov direct method of Razumikhin‐type condition and the principle of comparison, some sufficient conditions for globally pth moment exponentially ...
Fang Huang, Jianli Li
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