ABSTRACT
This chapter provides a survey of various aspects of the numerical solution of selected problems in linear systems, control, and estimation theory. Space limitations preclude an exhaustive survey and extensive list of references. The chapter highlights numerical aspects of the problems/algorithms, which is why we also spend time discussing appropriate numerical tools and techniques. It discusses a number of control and filtering problems that are of widespread interest in control. The chapter provides a very brief discussion of two concepts fundamentally important in numerical analysis: numerical stability and conditioning. Many of ad hoc algorithms work quite well on some problems but encounter numerical difficulties, often severe, when “pushed”. The reason for this is that little or no attention has been paid to the way algorithms perform in “finite arithmetic,” on a finite word length digital computer. The systems control, and estimation literature is replete with ad hoc algorithms to solve the computational problems which arise in the various methodologies.
