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Furthermore, our model helps us to understand why addition of an extra fold in the cavity could improve the stability of mode locked operation.
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The stability of modes at rest in non-linear mechanical systems which have one active mode undergoing chaotic oscillations is considered.
Sliding surface is designed and sufficient conditions for asymptotic stability of sliding mode dynamics are derived.
Besides, the analysis on both the stability of sliding mode dynamics and the reachability of sliding surface are made.
A model for ridge formation based upon the planar stability of a Mode I crack was proposed.
The sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities (LMIs).
Besides, both the reachability of the specified sliding surfaces and the stability of sliding mode dynamics are ensured despite the actuator degradation and Markovian jumping.
Based on a singular system approach and linear matrix inequality (LMI), a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given.
If a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form.
It has been shown that if a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form.
It has been shown that if a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form and thus the output transient performance indices are insensitive to parameter variations and external disturbances of the robotic manipulator.
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