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## Vibration control of vehicle engine-body systems with time delay: an LMI approach

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The objective of this chapter is to study the problem of vibration control analysis and synthesis in a vehicle engine-body vibration structure. It is assumed that the actuator is subject to a time-varying delay for control of bounce and pitch vibrations. Based on a Lyapunov-Krasovskii functional and using some free weighting matrices, delay-dependent sufficient conditions for designing desired state- and output-feedback controllers are given in terms of linear matrix inequalities (LMIs). The state- and output-feedback controllers, which guarantee asymptotic stability with a prescribed γ-level L2-gain (or H performance), are then developed directly instead of coupling the second-order model to a first-order system. The controller gains are determined by convex optimization over LMIs. Simulation results are included to demonstrate the validity and applicability of the technique.

Chapter Contents:

• Abstract
• 12.1 Introduction
• 12.2 The vehicle engine-body system
• 12.3 Problem formulation
• 12.4 Main results
• 12.4.1 State-feedback control design
• 12.4.2 Output-feedback control design
• 12.5 Simulation results
• 12.6 Conclusion
• References

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