Frequency domain design method for uncertain systems under some unknown-but-bounded disturbances

A frequency domain design methodology for a linear SISO uncertain system with control input and states constraints some unknown-but-bounded disturbances is developed. The maximum variation of the plant is transferred to the values of external disturbance at the plant output with a fixed nominal plant. Similarly, the control input and states constraints, expressed in the time domain with bandwidth limitation and mapped into a set of target transfer functions, will also be treated as the equivalent external disturbances upon being transferred to the output. The maximum variation of the desired output tolerance will be determined as the fixed values at some specified frequencies. Thus, the uncertain system design problem coping with the control input and states constraints under some unknown-but-bounded disturbances will become an equivalent external disturbance rejection problem. The uncertain plant tracking problems and the problem of uncertain systems with control input and states constraints under some unknown-but-bounded disturbance are respectively provided as illustrative examples