Results 211 to 220 of about 10,459,087 (262)
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On quadratic lyapunov functions
IEEE Transactions on Automatic Control, 2003A topological structure, as a subset of [0,2/spl pi/)/sup L//spl times//spl Ropf//sub +//sup n-1/, is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral ...
Jie Huang, Daizhan Cheng, Lei Guo
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1992
Publisher Summary This chapter elaborates the yield and applications of Lyapunov functions. It is applicable to ordinary differential equations and partial differential equations. It yields bounds on the solution in phase space. Even without solving a given differential equation, sometimes one can restrict the solution to be in a certain portion of ...
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Publisher Summary This chapter elaborates the yield and applications of Lyapunov functions. It is applicable to ordinary differential equations and partial differential equations. It yields bounds on the solution in phase space. Even without solving a given differential equation, sometimes one can restrict the solution to be in a certain portion of ...
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What is the most suitable Lyapunov function
, 2021P. Zhou, Xikui Hu, Zhigang Zhu, Jun Ma
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Lyapunov functionals and matrices
Annual Reviews in Control, 2010Abstract In this contribution we present some basic results concerning the computation of quadratic functionals with prescribed time derivatives for linear time delay systems. Some lower and upper bounds for the functionals are given. The functionals are defined by special matrix valued functions. These functions are called Lyapunov matrices.
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Lyapunov Functions and Martingales
1999The present chapter contains a potpourri of topics around potential theory and martingale theory. More exactly, it is a brief introduction to these topics, with the limited purpose of showing the power of martingale theory and the rich interplay between probability and analysis.
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Lyapunov Functions for Attractors
2017The concept of global uniform asymptotical stability of a set is defined through Lyapunov stability and uniformly attractivity. Yoshizawa’s Theorem on the existence of a Lyapunov function characterising global uniform asymptotical stability of a compact set is presented.
Peter E. Kloeden, Xiaoying Han
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Minimization of Lyapunov Functions
2016In this chapter we give a general overview of utilizing extremum seeking (ES) to stabilize a large class of systems, and discuss the strength of the approach for systems with unknown control directions, providing a stabilizing controller that is more robust than traditional Nussbaum type control.
Miroslav Krstic, Alexander Scheinker
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Applications of a family of lyapunov functions
Journal of Applied Mathematics and Mechanics, 2000The author considers the perturbed motion equations in the form \[ \begin{aligned} &A_1(x_1,\dot x_1,x_2,t)\ddot x_1 = B_1(x_1,\dot x_1,x_2,t);\\ &N_1(x_1,\dot x_1,x_2,t)\ddot x_2 = K_1(x_1,\dot x_1,x_2,t), \end{aligned}\tag{1} \] where \(A_1\) and \(N_1\) are \((n\times n)\)- and \((m\times m)\)-matrices, \(x_1\) and \(B_1\) are \(n\)-dimensional ...
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Construction of Lyapunov functions
1997Several designs in the preceding chapters require the knowledge of Lyapunov functions which need to be constructed during the design.
Mrdjan J. Jankovic +2 more
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2020
The present chapter is centered around the CLF paradigm that underlies the principal feedback design methods such as Bellman dynamic programming in optimal control and nonlinear \(\mathscr {H}_\infty \) approach in the robust synthesis. CLFs are first illustrated with quadratic forms, which result in a simple LMI criterion of the asymptotic stability ...
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The present chapter is centered around the CLF paradigm that underlies the principal feedback design methods such as Bellman dynamic programming in optimal control and nonlinear \(\mathscr {H}_\infty \) approach in the robust synthesis. CLFs are first illustrated with quadratic forms, which result in a simple LMI criterion of the asymptotic stability ...
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