The disturbance-rejection problem is to find a feedback control law for linear control systems such that the influence of disturbances is completely rejected from the output. In 1970 Wonham and Morse first studied this problem in the framework of the so-called geometric approach. On the other hand, in 1985 Ghosh studied parameter insensitive disturbance-rejection problems with state feedback and with dynamic compensator. In this paper we study the parameter insensitive disturbance-rejection problem with static incomplete-state feedback for linear multivariable systems in the framework of the geometric approach from the mathematical point of view. Necessary conditions and/or sufficient conditions for this problem to be solvable are presented. Finally an illustrative example is presented.

It is an important problem whether or not we can reject the disturbances from distributed parameter circuit. In order to analyze this problem structurally, it is necessary to investigate the basic equation of distributed parameter circuit in the framework of state space. Since the basic equation has two parameters for time and space, the state value belongs to an infinite-dimensional space. In this paper, the disturbance-rejection problems with incomplete state feedback and/or incomplete state feedback and feedforward for infinite-dimensional systems are studied in the framework of geometric approach. And under certain assumptions, necessary and/or sufficient conditions for these problems to be solvable are proved.

This paper presents a discrete-time multiple short-time Fourier transform (MSTFT) suitable for a time-frequency analysis and synthesis of discrete-time nonstationary signals. An overcomplete set of multiple windows in used for a frame constitution in l2 (Z) so that higher quality signal analysis and perfect reconstruction of the signal are achieved. A design method for a prototype window is given where the window can satisfy regularity condition and have a flexible, good time and frequency characteristic under constraint of the uncertainty principle. A dual frame is constructed using the prototype windows in the framework of a frame operator method. Efficient implementation structures for the MSTFT and its inverse transform appropriate for real time numerical processing is presented. Simulation results are given to illustrate the effectiveness for design of the MSTFT. The performance advantages as a new signal analysis tool are demonstrated with an experimental signal.