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We study the solution properties of a family of inverted pendulum systems driven by odd periodic forcing. Using the Schauder fixed point theorem, we show that the inverted pendulum with an odd periodic driving acceleration at the pivot always possesses an odd periodic solution. Fundamental to the production of good estimates is the development of a Green's function for an unstable harmonic oscillator...
This paper develops a unified Lyapunov approach to analysis of self-induced oscillations and stability for systems with piecewise linear components. For self-induced oscillation within a global or regional attractor, invariant level sets of a piecewise quadratic Lyapunov function are obtained to bound the attractor via linear matrix inequality based optimization. The analysis results for self-induced...
Two methods of the first Lyapunov exponent estimation for nonchaotic systems using time series are developed. Method's adequacy was tested on the typical systems. Analysis of the dependence between the estimation precision and the algorithm's parameters was performed.
A non-singular terminal sliding mode (TSM) controller design strategy is presented based on backstepping for a class of uncertain nonlinear system. By using a new inverse dynamic TSM surface, a control law with non-singularity is obtained, and the time from any initial system state to reach the sliding mode surface is proved to be finite. In order that the system output can track the expected signal...
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