The method of Lyapunov functions in problems of multistability of motion
The multistability of motion is defined as the property whereby different groups of variables describing the motion have different types of stability, e.g., one group has stability in the small, another has asymptotic stability, and another has boundedness etc. The method of Lyapunov functions is used to prove theorems on multistability which are then used to study the stability of motion of winged aircraft with respect to groups of variables. In existing definitions and studies of stability it is usually assumed that the phase coordinates have the same type of stability, e.g., asymptotic or uniform, etc. In practice, however, say when synthesizing aircraft trajectories, we need to take account of different requirements imposed on the behaviour of different groups of phase coordinates. For instance, when considering the space manoeuvres of an aircraft with constant load factor, it is important to obtain asymptotic stability with respect to the angles of attack and sideslip, while only uniform stability with respect to the angles of pitch, yaw, and rotation is needed. The angles of pitch, yaw, and rotation can themselves have any values, i.e., their stable behaviour is not required. In short, the individual coordinates or groups of coordinates of the same system can have different types of stability, say asymptotic or uniform. We then speak of the multistable motion of the system.
scientific article; zbMATH DE number 4110209