[ \beginalign* \dotx_1 &= f_1(x_1) + g_1(x_1)x_2 \ \dotx_2 &= f_2(x_1,x_2) + g_2(x_1,x_2)u \endalign* ]
If state space is the map, is the compass. Named after Aleksandr Lyapunov, this technique allows us to prove a system is stable without actually solving the complex differential equations. The Energy Analogy [ \beginalign* \dotx_1 &= f_1(x_1) + g_1(x_1)x_2 \
Controlling highly deformable structures with non-linear elasticity. 6. Conclusion x_2) + g_2(x_1
If you'd like to expand this into a more technical document, let me know: let me know: Ensuring smooth
Ensuring smooth, precise movement in limbs that have complex, changing centers of gravity. Power Grids:
Once on the surface, the system is insensitive to matched uncertainties and disturbances. The ugly: "Chattering"—high-frequency switching that can excite unmodeled dynamics (or break your actuator).