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Can I read Lie- and Chronologico-algebraic Tools for Studying Stability of Time-varying Systems on EtoBox?
Lie- and Chronologico-algebraic Tools for Studying Stability of Time-varying Systems by Andrey V. Sarychev is a Engineering article available to read on EtoBox.
What is Lie- and Chronologico-algebraic Tools for Studying Stability of Time-varying Systems about?
We will study stability and asymptotic stability for time-varying systems described by ODEs of the form ẋ = f( -1 t; x), where f(t; x) is 1-periodic with respect to t and ¿0 is a small parameter. Since the discovery of stabilizing e ect of vibration in the reverse pendulum example, there have been a lot of study regarding stability of such systems and design of fast-oscillating stabilizing feedback laws. In this paper we suggest an approach which is kind of high-order averaging procedure based on Lie algebraic formalism and the formalism of chronological calculus. This latter is a method of asymptotic analysis for ows generated by time-variant ODE. We apply the approach to study stability issues for linear and nonlinear systems. In particular, we derive conditions of stability for the second-and third-order linear di erential equations with periodic fast-oscillating coe cients, we study output-feedback stabilization of bilinear systems and consider high-order averaging procedure for nonlinear systems under homogeneity assumptions. At the end we study the problem of stabilization of nonholonomic (control-linear) systems by means of time-varying feedbacks.
Who reads Lie- and Chronologico-algebraic Tools for Studying Stability of Time-varying Systems?
It is typically read by researchers, students, and practitioners in Engineering.
- Author
- Andrey V. Sarychev
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0167-6911)
- Published
- 2001
- Language
- EN
- Field
- Engineering (Physical Sciences)