Qualitative theory of hybrid dynamical systems
نویسندگان
چکیده
matrices and M matrices instead. Though there are a good monograph (Berman & Plemmons, 1994) and an article (Fiedler & PtA ak, 1962), these subjects are not covered by a standard linear algebra course. Notwithstanding the above points, I strongly recommend the book because it covers important properties of positive systems, and it includes wide range of applications. I particularly :nd the annotated bibliography useful and informative. The book includes many relevant problems, which helps readers to have accurate images of theoretical results. The study on positive nonlinear systems is important, and I agree with the authors’ opinion in the Conclusion that it makes sense to acquire a sound background on positive linear systems before studying positive nonlinear systems.
منابع مشابه
Fractional dynamical systems: A fresh view on the local qualitative theorems
The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...
متن کاملDynamical Behavior of a Rigid Body with One Fixed Point (Gyroscope). Basic Concepts and Results. Open Problems: a Review
The study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1) to outline the characteristic features of...
متن کاملTowards a stability theory of general hybrid dynamical systems1
In recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time. For such systems we introduced the usual concepts of Lyapunov and Lagrange stability. We showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems ...
متن کاملStability Theory for Hybrid Dynamical Systems - Automatic Control, IEEE Transactions on
Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior in different parts of a system (e.g., continuous-time dynamics, discrete-time dynamics, jump phenomena, switching and logic commands, and the like) are of great current interest. In the present paper we first formulate a model for hybrid dynamical systems which covers a very large class of systems an...
متن کاملA survey on piecewise-linear models of regulatory dynamical systems
Recent developments in understanding the various regulatory systems, especially the developments in biology and genomics, stimulated an interest in modelling such systems. Hybrid systems, originally developed for process control applications, provide advances in modelling such systems.A particular class of hybrid systems which are relatively simpler to analyze mathematically but still capable o...
متن کاملPoincaré-Bendixson Theorem for Hybrid Systems
The Poincaré-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincaré-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincaré return map, a useful object for the stabili...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002