Short Time Stability In Linear Time Varying Systems

Short-time Stability in Linear Time-varying Systems

The concept of short-time stability finds application in missile and satellite systems where operating times are often of finite duration. Short-time stability assures, in a finite time interval, that all inputs bounded by a prescribed constant Greek epsilon result in outputs bounded by a second prescribed constant. The study of short-time stability is divided into two categories: undriven systems and driven systems. Undriven systems are represented by a set of differential equations. Sufficient conditions for short-time stability are given in terms of the coefficients. Driven systems are represented by their impulse response. A necessary and sufficient condition for short-time stability in driven systems is given directly in terms of impulse response. Sufficient conditions for short-time stability in feedback systems, in terms of the open loop impulse response are also included. In addition the concept of shorttime C-equivalence, essentially a structural stability concept, is introduced. Necessary and sufficient conditions for two systems to be short-time C-equivalent are presented. (Author).

Linear Time-varying Systems

Analysis of Periodically Time-Varying Systems

Many of the practical techniques developed for treating systems described by periodic differential equations have arisen in different fields of application; con sequently some procedures have not always been known to workers in areas that might benefit substantially from them. Furthermore, recent analytical methods are computationally based so that it now seems an opportune time for an applications-oriented book to be made available that, in a sense, bridges the fields in which equations with periodic coefficients arise and which draws together analytical methods that are implemented readily. This book seeks to ftll that role, from a user's and not a theoretician's view. The complexities of periodic systems often demand a computational approach. Matrix treatments therefore are emphasized here although algebraic methods have been included where they are useful in their own right or where they establish properties that can be exploited by the matrix approach. The matrix development given calls upon the nomenclature and treatment of H. D'Angelo, Linear Time Varying Systems: Analysis and Synthesis (Boston: Allyn and Bacon 1970) which deals with time-varying systems in general. It is recommended for its modernity and comprehensive approach to systems analysis by matrix methods. Since the present work is applications-oriented no attempt has been made to be complete theoretically by way of presenting all proofs, existence theorems and so on. These can be found in D'Angelo and classic and well-developed treatises such as McLachlan, N. W. : Theory and application of Mathieu functions.