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Integral Characterizations of Uniform Asymptotic and Exponential Stability with Applications
Mathematics of Control, Signals, and Systems, 2002Integral characterizations of uniform global asymptotic stability (UGAS) and uniform global exponential stability (UGES) for time-varying differential inclusions are proved. These integral characterizations are used to conclude UGAS from uniform global stability (UGS) and suitable properties of the derivatives of a family of functions.
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Relaxed persistency of excitation for uniform asymptotic stability
IEEE Transactions on Automatic Control, 2001The authors of this paper propose a relaxed definition for persistence of excitation (uniform persistence of excitation), a property crucial for some stability analyses of parameter identification algorithms and adaptive control systems. The relaxed definition is used to establish uniform global asymptotic stability and uniform local exponential ...
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ON UNIFORM ASYMPTOTIC STABILITY OF INFINITE DELAY DIFFERENCE EQUATIONS
Chinese Annals of Mathematics Series B, 2001The author considers the infinite delay difference equation \[ x(n+1)= F\bigl(n,x_n (\cdot)\bigr) \] with \(x_n(s)= x(n+s)\), \(s\leq 0\), \(F:\mathbb{Z} \times{\mathcal C}_H \to\mathbb{R}^k\) where \({\mathcal C}_H= \{\varphi\in {\mathcal C},\|\varphi \|< H\}\) and \({\mathcal C}\) is the space of the sequences \(\{\varphi_k \}_k ...
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Uniform asymptotic stability of hybrid dynamical systems with delay
IEEE Transactions on Automatic Control, 2003We formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via a Lyapunov-Razumikhin technique.
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