Weitere Kapitel dieses Buchs durch Wischen aufrufen
This chapter is focussed on a nonautonomous version of the well-known Yakubovich Frequency Theorem, which was originally formulated for linear control systems x′ = A(t) x + B(t) u with time-periodic coefficients. The extension of this theorem to the nonautonomous category is formulated in terms of a linear-quadratic optimization problem involving an indefinite quadratic function of x and u with nonperiodic coefficients. Methods discussed in the previous chapters will be systematically applied in this one. In particular, the Frequency Condition and the Nonoscillation Condition of the periodic case are rewritten in terms involving the occurrence of exponential dichotomy together with the properties of the Weyl function associated to the solutions bounded at \(+\infty \). They can also be formulated in terms of properties of the rotation number. The chapter also contains a description of two scenarios in which the Frequency Condition and the Nonoscillation Conditions hold: these are characterized, roughly speaking, by the presence or absence of the uniform weak disconjugacy property discussed in Chap. 5
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- Nonautonomous Control Theory: A General Version of the Yakubovich Frequency Theorem
- Chapter 7
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