Synthesis of 3-rd Order Performance-Optimal Stabilizaton System

An urgent problem is solved for synthesis of the 3-rd order performanceoptimal control of a linear object with a differential equation including a derivative in its right part. A problem is considered for translating an arbitrary initial state of the controlled object into the origin of the coordinate system and holding the object in the zero state. The approximation of the switch surface is performed which essentially simplifies the controller structure. Obtained results can be applied for synthesis of the algorithm for controlling any 3-rd order linear objects, whose equations include a derivative of input action.