In this paper we study ISS-like properties of infinite dimensional discrete time systems and compare them with their continuous time counterparts available in the literature. New characterizations of such properties a...
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In this paper we study ISS-like properties of infinite dimensional discrete time systems and compare them with their continuous time counterparts available in the literature. New characterizations of such properties are derived in this work. We discuss differences between discrete and continuous time systems in view of their robust stability and demonstrate the corresponding properties by means of examples.
The Input-to-State stability (ISS) of homogeneous evolution equations with unbounded linear operators and locally Lipschitz nonlinearities in Banach spaces is studied using a new homogeneous converse Lyapunov theorem....
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The Input-to-State stability (ISS) of homogeneous evolution equations with unbounded linear operators and locally Lipschitz nonlinearities in Banach spaces is studied using a new homogeneous converse Lyapunov theorem. It is shown that, similarly to finite-dimensional models, uniform asymptotic stability of an unperturbed homogeneous system guarantees its ISS with respect to homogeneously involved exogenous inputs. (C) 2021 Elsevier Ltd. All rights reserved.
The existence of a locally Lipschitz continuous homogeneous Lyapunov function is proven for a class of asymptotically stable homogeneous infinite dimensional systems with unbounded nonlinear operators. (C) 2020 Elsevi...
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The existence of a locally Lipschitz continuous homogeneous Lyapunov function is proven for a class of asymptotically stable homogeneous infinite dimensional systems with unbounded nonlinear operators. (C) 2020 Elsevier B.V. All rights reserved.
The existence of homogeneous Lyapunov function for a stable homogeneous ordinary differential equation (ODE) is proven by V. Zubov in 1958 and refined by L. Rosier in 1992. The present paper proposes an extension of t...
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The existence of homogeneous Lyapunov function for a stable homogeneous ordinary differential equation (ODE) is proven by V. Zubov in 1958 and refined by L. Rosier in 1992. The present paper proposes an extension of this result to evolution equations in Banach spaces. Copyright (C) 2020 The Authors.
This paper introduces a simplified mechanical model of pressure relief valves extended by a downstream pipe. The distributedparameter model of the system is presented and transformed into a system of neutral delay di...
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This paper introduces a simplified mechanical model of pressure relief valves extended by a downstream pipe. The distributedparameter model of the system is presented and transformed into a system of neutral delay differential equations. It is shown that the time delay is proportional to the length of the downstream pipe. The analytical investigation of the system proves the stabilizing effect of the pipe length, which is relevant in the safe operation of these valves.
The existence of homogeneous Lyapunov function for a stable homogeneous ordinary differential equation (ODE) is proven by V. Zubov in 1958 and refined by L. Rosier in 1992. The present paper proposes an extension of t...
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The existence of homogeneous Lyapunov function for a stable homogeneous ordinary differential equation (ODE) is proven by V. Zubov in 1958 and refined by L. Rosier in 1992. The present paper proposes an extension of this result to evolution equations in Banach spaces.
The paper is concerned with the PI control regulation of a star-shaped network of systems governed by hyperbolic partial differential equations. The control input and measured output are on the boundary. First, each s...
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The paper is concerned with the PI control regulation of a star-shaped network of systems governed by hyperbolic partial differential equations. The control input and measured output are on the boundary. First, each system of the network is linearized and diagonalized with Riemann invariants. Then, by using Lyapunov direct method, the PI controller is proposed for a single system. Finally, we extend the PI control design for the star-shaped network of n subsystems. The exponential stability and output regulation of closed-loop systems are all proven with the aid of a strict Lyapunov functional. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
An unconditionally stable finite difference scheme for systems whose dynamics are described by a fourth-order partial differential equation is developed using a regular hexagonal grid. The scheme is motivated by the w...
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An unconditionally stable finite difference scheme for systems whose dynamics are described by a fourth-order partial differential equation is developed using a regular hexagonal grid. The scheme is motivated by the w...
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An unconditionally stable finite difference scheme for systems whose dynamics are described by a fourth-order partial differential equation is developed using a regular hexagonal grid. The scheme is motivated by the well-known Crank-Nicolson discretization that was originally developed for second-order systems and it is used in this paper to develop a discrete in time and space model of a deformable mirror as a basis for control law design. As one example, the resulting model is used for iterative learning control law design and supporting numerical simulations are given. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
The paper is concerned with the PI control regulation of a star-shaped network of systems governed by hyperbolic partial differential equations. The control input and measured output are on the boundary. First, each s...
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