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

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Systems Satisfying the Conditions of LaSallecally stable, it is still desirable to be able to construct a strict Lyapunov function for the system, e.g., for robustness analysis and feedback design. In this chapter, we give two more methods for constructing strict Lyapunov functions, which apply to cases where asymptotic stability is already k

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Strictification: Basic Resultsve analogs for time-varying systems. In general, these involve replacing the negative semi-definite function of the state in the right side of the non-strict Lyapunov decay condition with a . of a negative semi-definite function of the state and a suitable time-varying parameter. We assume that the

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Backstepping for Time-Varying Systemso a wide family of globally asymptotically stabilizing control laws, and it makes it possible to address robustness issues and solve adaptive control problems. This chapter begins with a review of classical backstepping for time-invariant systems. We then give several extensions that lead to timevar

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Adaptively Controlled Systemsnamics are completely known. However, there are important cases where the system parameters are unknown, and where the objectives are to simultaneously (a) design controllers that force the trajectories to track a prescribed reference trajectory and (b) estimate the unknown parameters. In this chapt

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Rapidly Time-Varying Systemswith two continuous time scales, one faster than the other. Systems of this kind are called either rapidly time-varying systems or slowly time-varying systems. The presence of multiple time scales significantly complicates the problem of constructing global strict Lyapunov functions. In this chapter

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Slowly Time-Varying Systemsentary problem of explicitly constructing strict Lyapunov functions for . time-varying continuous time systems. As in the case of rapidly time-varying systems, slowly time-varying systems involve two continuous time scales, one faster than the other. However, the methods for constructing strict Lyap

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Hybrid Time-Varying Systemsimes readily available non-strict Lyapunov functions. This led to more explicit formulas for stabilizing feedbacks, as well as explicit quantizations of the effects of uncertainties, in the context of ISS. However, there are many cases where continuous and discrete time systems in and of themselves

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Urogenitaltrakt, Retroperitoneum, Mammaov functions, in the directions of the vector fields that define the systems. Our second method uses our continuous time Matrosov Theorem from Chap. 3. We illustrate our approach by constructing a strict Lyapunov function for an appropriate error dynamics involving the Lotka-Volterra Predator-Prey System.

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Stefano Stanghellini,Sergio Copiellong this more complicated decay condition into explicit strict Lyapunov functions. In this chapter, we provide methods for solving this and related problems, including the construction of ISS Lyapunov functions for time-varying systems. We apply our work to stabilization problems for rotating rigid bodies and underactuated ships.