## Abstract

In this study, three strategies based on infinite-dimensional Floquet theory, Chebyshev spectral collocation, and the Lyapunov–Floquet transformation (LFT) are proposed for optimal feedback control of linear time periodic delay differential equations using periodic control gains. First, a periodic-gain discrete-delayed feedback control is implemented where optimization of the control gains is included to obtain the minimum spectral radius of the closed-loop response. Second, a large set of ODEs is obtained using the Chebyshev spectral continuous time approximation, after which optimal (time-varying LQR) control is used to obtain a periodic-gain distributed-delayed feedback control. The third strategy involves the use of both CSCTA and the reduced LFT, along with either pole-placement or time-invariant LQR used on a linear time invariant auxiliary system, to obtain a periodic-gain non-delayed feedback control that asymptotically stabilizes the original system. The delayed Mathieu equation is used as an illustrative example for all three control strategies.

Original language | English (US) |
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Pages (from-to) | 102-118 |

Number of pages | 17 |

Journal | International Journal of Dynamics and Control |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2014 |

## Keywords

- Chebyshev spectral collocation
- Floquet theory
- Lyapunov–Floquet transformation
- Optimal feedback control
- Periodic delay differential equations

## ASJC Scopus subject areas

- Control and Systems Engineering
- Civil and Structural Engineering
- Modeling and Simulation
- Mechanical Engineering
- Control and Optimization
- Electrical and Electronic Engineering