Motorcycle suspension design using matrix inequalities and passivity constraints

Amrit Sharma, David J.N. Limebeer

Research output: Contribution to journalReview articlepeer-review

4 Citations (Scopus)


This paper presents a design methodology for the suspension system of a novel aerodynamically efficient motorcycle. Since the machines layout and the riders seating position are unconventional, several aspects of the machine design, including the suspension, must be reviewed afresh. The design process is based on matrix inequalities that are used to optimise a road-grip objective function - others could be used equally well. The design problem is cast as the minimisation of an H 2 cost with passivity constraints imposed on the suspension transference. The resulting bilinear matrix inequality problem is solved using a locally optimal iterative algorithm. The matrix inequality-type characterisation of positive real functions permits the optimisation of the suspension system over an entire class of passive admittances. Torsional springs, dampers and inerters are then used to construct networks corresponding to the optimal (positive real) admittances. Networks of first, second, third and fourth orders are considered, and an argument based on the compromise between complexity and improved grip is made for the most suitable suspension configuration. Finally, the effects of improved road grip on the stability of the vehicles lateral dynamics are analysed.

Original languageEnglish
Pages (from-to)377-393
Number of pages17
JournalVehicle System Dynamics
Issue number3
Publication statusPublished - Mar 2012
Externally publishedYes


  • matrix inequalities
  • motorcycle dynamics
  • passive circuit theory
  • suspension design
  • suspension optimisation

ASJC Scopus subject areas

  • Automotive Engineering
  • Safety, Risk, Reliability and Quality
  • Mechanical Engineering


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