Lyapunov–Krasovskii functionals for scalar time delay equations
Systems & Control Letters, 2004Abstract In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar time delay equation is considered. The functionals depend on a scalar function which satisfies a time delay equation. It is shown that the scalar function satisfies also a high order delay free differential equation.
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Estimating stable delay intervals with a discretized Lyapunov–Krasovskii functional formulation
Automatica, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yongmin Li 0003 +3 more
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Complete Type Lyapunov-Krasovskii Functionals
2004In this chapter we give a general description of the complete type quadratic Lyapunov-Krasovskii functionals. Special Lyapunov matrices associated with the functionals are also defined. Uniqueness conditions, as well as a numerical scheme for computation of the Lyapunov matrices, are discussed. Some robust stability conditions. based on the functional,
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The Relationship Between Augmented Lyapunov-Krasovskii Functionals and Estimated Inequalities
International Journal of Control, Automation and SystemsCan Zhao, Shouming Zhong, Daixi Liao
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Discretized Lyapunov-Krasovskii Functional for Systems With Multiple Delay Channels
ASME 2008 Dynamic Systems and Control Conference, Parts A and B, 2008Many practical systems have a large number of state variables but only a few components have time delays. These delay components are often scalar or low dimensional, and involve single time delay in each component. A coupled differential-difference equation is well suited to formulate such systems.
Hongfei Li, Keqin Gu
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Stability of Systems With Uncertain Delays: A New “Complete” Lyapunov–Krasovskii Functional
IEEE Transactions on Automatic Control, 2006Stability of linear systems with uncertain time-varying delay is considered in the case, where the nominal value of the delay is constant and nonzero. Recently a new construction of Lyapunov-Krasovskii functionals (LKFs) has been introduced: To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the
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Some remarks on Lyapunov-Krasovskii functionals and reduction approach for input delay compensation
2012 American Control Conference (ACC), 2012For linear systems with pointwise or distributed delays in the inputs which are stabilized through the reduction approach, we propose a new construction technique of Lyapunov-Krasovskii functionals. These functionals allow us to establish the ISS property of the closed-loop systems relative to additive disturbances.
Mazenc, Frédéric +2 more
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Complete type Lyapunov-Krasovskii functionals with a given cross term in the time derivative
Proceedings of the 44th IEEE Conference on Decision and Control, 2006A general expression for the complete type quadratic Lyapunov-Krasovskii functional with a given cross term in the time derivative is presented. Some robust stability conditions and exponential estimates are obtained.
Sabine Mondié +2 more
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Construction of Lyapunov–Krasovskii Functionals for Nonlinear Mechanical Systems with Delay
2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB), 2020New constructions of Lyapunov–Krasovskii functionals are proposed for certain classes of nonlinear mechanical systems with delay. With the aid of these functionals, stability conditions of equilibrium positions and estimates of transient times, as well as stability conditions for corresponding systems with switching force fields are obtained.
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New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems
Systems & Control Letters, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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