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In this paper, we consider the stability of periodic solution of linear systems with state jump. While this model is general enough to describe the complex dynamics of a class of hybrid systems including the (approximated) biped passive compass walking, it also retains the tractability for the analytic mathematical treatment. With an appropriate definition of the stability, we can justify the use of Poincare map in the analysis. The formula for the linearized Poincare map, which determines the local stability of the periodic solution, is given. The effect of feedback control (for the case that the nominal trajectory is known) is also discussed.

On Periodic Motion of Linear Systems with State Jump-Modelling, Stability Analysis and Feedback Control of Compass Walking