By investigating the properties of the natural state, this book presents an analysis of input-output systems with regard to the mathematical concept of state. The state of a system condenses the effects of past inputs to the system in a useful manner. Thismonograph emphasizes two main properties of the natural state;the first has to do with the possibility of determining the input-output system from its natural state set and the second deals with differentiability properties involving the natural state inherited from the input-output system, including differentiability of the natural state...

This book defines and develops the generalized adjoint of an input-output system. It is the result of a theoretical development and examination of the generalized adjoint concept and the conditions under which systems analysis using adjoints is valid. Results developed in this book are useful aids for the analysis and modeling of physical systems, including the development of guidance and control algorithms and in developing simulations. The generalized adjoint system is defined and is patterned similarly to adjoints of bounded linear transformations. Next the elementary properties of the...