Decentralized stabilization in presence of non structurally fixed modes

Abstract

In this chapter, it is shown that systems with unstable non structurally fixed modes can be stabilized by using time-varying or non-linear feedback control laws which preserve the feedback structure constraints. The use of sample and hold (WAN-82) (OZG-85), the application of piecewise constant or sinusoīdal feedback laws (AND-81b) (PUR-82), and the introduction of almost periodic vibrations on the system parameters (TRA-85) or through the feedback (RUN-85) are different stabilizing approaches which are presented in this chapter.

Obviously, the sacrifice of linerarity or time invariance of the control brings difficulties in the analysis of such controlled systems, even of small dimensionality. Time-varying systems analysis methods or averaging schemes must be used.

On another hand the implementation of such control laws may be practically unconvenient. Consequently it is the authors believe that relaxing the structure constraints (if possible) is a more realistic approach. This approach is investigated in the following chapter and several algorithms are provided.