Inverted pendulum stabilization: characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains

DOI10.1016/j.sysconle.2015.03.002zbMath1327.93322OpenAlexW561938405MaRDI QIDQ899107

Islam Boussaada, Irinel-Constantin Morărescu, Silviu Iulian Niculescu

Publication date: 21 December 2015

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2015.03.002

zbMATH Keywords

stabilitytime-delaynormal formsinverted pendulumcenter manifolddelayed feedbacklocal bifurcation analysisnonhyperbolic dynamics

Mathematics Subject Classification ID

Eigenvalue problems (93B60) Bifurcation theory for ordinary differential equations (34C23) Asymptotic stability in control theory (93D20) Control of mechanical systems (70Q05) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (11)

Passivity-based PI control of first-order systems with I/O communication delays: a frequency domain analysis ⋮ Subharmonic bifurcations and chaotic motions for a class of inverted pendulum system ⋮ Conditions for stabilizability of time‐delay systems with real‐rooted plant ⋮ Critical parameters for the robust stabilization of the inverted pendulum with reaction delay: State feedback versus predictor feedback ⋮ On the Codimension of the Singularity at the Origin for Networked Delay Systems ⋮ Bi‐homogeneous observers for uncertain 1‐DOF mechanical systems ⋮ A Review on Multiple Purely Imaginary Spectral Values of Time-Delay Systems ⋮ Bogdanov–Takens and Triple Zero Bifurcations of Coupled van der Pol–Duffing Oscillators with Multiple Delays ⋮ Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design ⋮ Control design and experimental validation for flexible multi-body systems pre-compensated by inverse shapers ⋮ Characterizing the codimension of zero singularities for time-delay systems. A link with Vandermonde and Birkhoff incidence matrices

Uses Software

• Maple

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