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The notions of phi(0)-stability, (h(0),h)-stability integral and eventual stability of nonlinear systems of ordinary differential equations (ODE's) are introduced. Our aim in this paper is to improve and extend these notions to ne...
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The notions of phi(0)-stability, (h(0),h)-stability integral and eventual stability of nonlinear systems of ordinary differential equations (ODE's) are introduced. Our aim in this paper is to improve and extend these notions to new types of stability namely, phi(0),-L-p-stability, (h(0),h)-integral stability and (h(0),h)-eventual stability of systems of ODE's, respectively, and given some criteria. Our technique depends on Liapunov direct method. (C) 2000 Elsevier Science Inc. All rights reserved. [References: 8]
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We revisit the theorem of Barker, Berman and Plemmons on the existence of a diagonal quadratic Lyapunov function for a stable linear time-invariant (LTI) dynamical system [G.P. Barker. A. Berman, R.J. Plemmons, Positive diagonal s...
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We revisit the theorem of Barker, Berman and Plemmons on the existence of a diagonal quadratic Lyapunov function for a stable linear time-invariant (LTI) dynamical system [G.P. Barker. A. Berman, R.J. Plemmons, Positive diagonal solutions to the Lyapunov equations, Linear and Multilinear Algebra 5(3) (1978) 249-256]. We use recently derived results to provide an alternative roof of this result and to derive extensions. (C) 2008 Elsevier Inc. All rights reserved.
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In this paper, a class of linear systems affected by parameter variations, additive noise and persistent disturbances is considered. The problem of designing a set-valued state observer, which estimates a region containing the rea...
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In this paper, a class of linear systems affected by parameter variations, additive noise and persistent disturbances is considered. The problem of designing a set-valued state observer, which estimates a region containing the real state for each time instant, is investigated. The techniques for designing the observer are based on positive invariant set theory. By constructing a set-induced Lyapunov function, it is shown that the estimation error converges exponentially to a given compact set with an assigned rate of convergence. [References: 18]
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In this study, we propose a new method to design a smooth implicit control Lyapunov function and a smooth control law for a multi-integrator system with an input constraint. The proposed controller is almost linear near the origin...
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In this study, we propose a new method to design a smooth implicit control Lyapunov function and a smooth control law for a multi-integrator system with an input constraint. The proposed controller is almost linear near the origin, and it tends to a homogeneous controller of the previous implicit Lyapunov function methods as the state goes to infinity. The proposed method can be used for the backstepping method with a restricted virtual input, which is a nonlinear function of the state, and the desired virtual input is designed as a bounded function. Furthermore, we apply our method to the control of a magnetic levitation system, and a simulation result presents the advantage of the proposed method. (C) 2020 The Authors. Published by Elsevier B.V.
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We show in this paper that certain types of polytope of polynomials have parameter-dependent Lyapunov functions. The functions are quadratic ones with coefficients being just the Hermite matrix whose positive definiteness ensures ...
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We show in this paper that certain types of polytope of polynomials have parameter-dependent Lyapunov functions. The functions are quadratic ones with coefficients being just the Hermite matrix whose positive definiteness ensures Hurwitz stability of polynomials. It is demonstrated that the polytopes of polynomials have corresponding polytopes of Lyapunov functions and that thereby stability of the polytopes comes from that of their extreme polynomials. The results obtained lead to an alternative proof for some known results, including weak Kharitonov's theorem, via Lyapunov route and would possibly provide some tool for searching links between Lyapunov approach and established frequency domain results on stability of systems with structured uncertainties. [References: 5]
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摘要 :
We show in this paper that certain types of polytope of polynomials have parameter-dependent Lyapunov functions. The functions are quadratic ones with coefficients being just the Hermite matrix whose positive definiteness ensures ...
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We show in this paper that certain types of polytope of polynomials have parameter-dependent Lyapunov functions. The functions are quadratic ones with coefficients being just the Hermite matrix whose positive definiteness ensures Hurwitz stability of polynomials. It is demonstrated that the polytopes of polynomials have corresponding polytopes of Lyapunov functions and that thereby stability of the polytopes comes from that of their extreme polynomials. The results obtained lead to an alternative proof for some known results, including weak Kharitonov's theorem, via Lyapunov route and would possibly provide some tool for searching links between Lyapunov approach and established frequency domain results on stability of systems with structured uncertainties. [References: 5]
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In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with two delays and with a P-controller is presented. The value of integral quadratic performance index of quality is equal to th...
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In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with two delays and with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix.
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New sufficient conditions for the stability and asymptotic stability of a nonlinear impulsive system are established. An essentially nonlinear system is considered as an example to illustrate the results obtained.
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In Kalitine (RAIRO Automatique/Systems Anal. Control 16(3) (1982) 275) the use of semi-definite Lyapunov functions for exploring the local stability of autonomous dynamical systems has been introduced. In this paper, we give an ex...
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In Kalitine (RAIRO Automatique/Systems Anal. Control 16(3) (1982) 275) the use of semi-definite Lyapunov functions for exploring the local stability of autonomous dynamical systems has been introduced. In this paper, we give an extension of the results of Kalitine (1982) that allows to study the local stability of nonautonomous differential systems. We give an application to the algebraic Riccati equation. (C) 2002 Elsevier Science Ltd. All rights reserved. [References: 16]
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A Perron type theorem about the existence of the strict Lyapunov exponents of the solutions of retarded functional differential equations is established. (c) 2005 Elsevier Inc. All rights reserved.
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