Stability analysis and controller designs for linear time periodic systems using normal forms

Susheelkumar C. Subramanian, Sangram Redkar

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The investigation of stability bounds for linear time periodic systems have been performed using various methods in the past. The Normal Forms technique has been predominantly used for analysis of nonlinear equations. In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique for a linear system with time periodic coefficients. Moreover, the authors utilize the Normal Forms technique to transform a linear time periodic system to a time-invariant system by using near identity transformation, similar to the Lyapunov Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation and near identity transformations to enable the application of time independent Normal Forms directly without the use of detuning or book-keeping parameter. This method provides a closed form analytical expression for the state transition matrix with the elements as a function of time. Additionally, stability analysis is performed on the transformed system and the resulting transitions curves are compared with that of numerical simulation results. Furthermore, a linear feedback controller design is discussed based on the stability bounds and the implementation of an effective feedback controller for an unstable case is discussed. The theory is validated and verified using numerical simulations of temporal variation of a simple linear Mathieu equation.

Original languageEnglish (US)
Title of host publicationIntelligent Transportation/Vehicles; Manufacturing; Mechatronics; Engine/After-Treatment Systems; Soft Actuators/Manipulators; Modeling/Validation; Motion/Vibration Control Applications; Multi-Agent/Networked Systems; Path Planning/Motion Control; Renewable/Smart Energy Systems; Security/Privacy of Cyber-Physical Systems; Sensors/Actuators; Tracking Control Systems; Unmanned Ground/Aerial Vehicles; Vehicle Dynamics, Estimation, Control; Vibration/Control Systems; Vibrations
PublisherAmerican Society of Mechanical Engineers
ISBN (Electronic)9780791884287
StatePublished - 2020
EventASME 2020 Dynamic Systems and Control Conference, DSCC 2020 - Virtual, Online
Duration: Oct 5 2020Oct 7 2020

Publication series

NameASME 2020 Dynamic Systems and Control Conference, DSCC 2020


ConferenceASME 2020 Dynamic Systems and Control Conference, DSCC 2020
CityVirtual, Online


  • Control system
  • Linear time periodic systems
  • Normal forms
  • Stability analysis

ASJC Scopus subject areas

  • Artificial Intelligence
  • Energy Engineering and Power Technology
  • Aerospace Engineering
  • Automotive Engineering
  • Biomedical Engineering
  • Control and Systems Engineering
  • Mechanical Engineering
  • Control and Optimization


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