Titlebook: Constructions of Strict Lyapunov Functions; Michael‘Malisoff,Frédéric Mazenc Book 2009 Springer-Verlag London 2009 Lyapunov Analysis.Lyapu

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Guido Eilenberger,Sascha Haghanie explicit ISS Lyapunov functions, in terms of given non-strict Lyapunov functions for the continuous and discrete subsystems, as well as a hybrid version of Matrosov’s Theorem. We illustrate our results using a hybrid version of the identification dynamics we saw in previous chapters.

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0178-5354 for quantifying the effects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples..978-1-4471-5782-3978-1-84882-535-2Series ISSN 0178-5354 Series E-ISSN 2197-7119

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Matrosov Conditions: Simple Caseons for time-invariant systems that satisfy appropriate Matrosov Conditions. In Chapters 8 and 12, we generalize to much more complex time-varying systems, including Matrosov type theorems for hybrid systems.

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Jurdjevic-Quinn Conditionsb) our methods apply to Hamiltonian systems, which commonly arise in mechanical engineering. We illustrate our work using a two-link manipulator model, as well as an integral input-to-state stability result.

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Hybrid Time-Varying Systemse explicit ISS Lyapunov functions, in terms of given non-strict Lyapunov functions for the continuous and discrete subsystems, as well as a hybrid version of Matrosov’s Theorem. We illustrate our results using a hybrid version of the identification dynamics we saw in previous chapters.

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Background on Nonlinear Systemsy, including the input-to-state stability paradigm. An important feature is the distinction between uniform and non-uniform stability for timevarying systems. We also include an overview of the problem of stabilization of nonlinear systems, including the “virtual” obstacles to stabilization imposed

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Jurdjevic-Quinn Conditions amplitude. It requires certain algebraic conditions on the Lie derivatives of a suitable non-strict Lyapunov function, in the directions of the vector fields that define the system. The non-strictness of the Lyapunov function is an obstacle to proving robustness, since robustness analysis typically