Exponential Estimates in Averaging and Homogenisation

Abstract This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.

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Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type

Symmetry ◽

10.3390/sym12101613 ◽

2020 ◽

Vol 12 (10) ◽

pp. 1613

Author(s):

Mun-Jin Bae ◽

Chan-Ho Park ◽

Young-Ho Kim

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Existence And Uniqueness ◽

Neutral Type ◽

Sufficient Conditions ◽

Exponential Estimates ◽

Analysis Theory ◽

Linear Growth Condition ◽

Uniqueness Of The Solution ◽

The Uniqueness Theorem

The main purpose of this study was to demonstrate the existence and the uniqueness theorem of the solution of the neutral stochastic differential equations under sufficient conditions. As an alternative to the stochastic analysis theory of the neutral stochastic differential equations, we impose a weakened Ho¨lder condition and a weakened linear growth condition. Stochastic results are obtained for the theory of the existence and uniqueness of the solution. We first show that the conditions guarantee the existence and uniqueness; then, we show some exponential estimates for the solutions.

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Application of M-matrices in construction of exponential estimates for solutions to the Cauchy problem for systems of linear difference and differential equations

Siberian Advances in Mathematics ◽

10.3103/s1055134414040026 ◽

2014 ◽

Vol 24 (4) ◽

pp. 240-260 ◽

Cited By ~ 1

Author(s):

N. V. Pertsev

Keyword(s):

Cauchy Problem ◽

Differential Equations ◽

Exponential Estimates ◽

The Cauchy Problem

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Exponential Estimates for the Conjugate Function on Locally Compact Abelian Groups

Canadian Mathematical Bulletin ◽

10.4153/cmb-1990-006-9 ◽

1990 ◽

Vol 33 (1) ◽

pp. 34-44

Author(s):

Nakhlé Habib Asmar

Keyword(s):

Compact Support ◽

Weak Type ◽

Conjugate Function ◽

Locally Compact Abelian Group ◽

Locally Compact ◽

Character Group ◽

Exponential Estimates ◽

Compact Abelian Groups ◽

The Hilbert Transform ◽

Almost All

AbstractLet G be a locally compact Abelian group, with character group X. Suppose that X contains a measurable order P. For the conjugate function of f is the function whose Fourier transform satisfies the identity for almost all χ in X where sgnp(χ) = - 1 , 0, 1, according as We prove that, when f is bounded with compact support, the conjugate function satisfies some weak type inequalities similar to those of the Hilbert transform of a bounded function with compact support in ℝ. As a consequence of these inequalities, we prove that possesses strong integrability properties, whenever f is bounded and G is compact. In particular, we show that, when G is compact and f is continuous on G, the function is integrable for all p > 0.

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