The idea is that, under suitable assumptions, the interconnection of dissipative systems is lyapunov stable. Stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for. Hence, by establishing l 2gain or passivity properties of piecewise linear systems we can hope to establish stability of interconnections by invoking small gain and passivity theorems. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. Dissipativity reinforcement in interconnected systems.
In this book we address networks where the subsystems are. We provide a stability condition for interconnections of such systems. Abstract \emphinternational journal of robust and nonlinear control, vol. Inputoutputtostate stability tools for hybrid systems and their interconnections. Provides complete coverage of both the lyapunov and inputoutput stability theories, ina readable, concise manner. Abstractthis paper is concerned with the stability analysis of the interconnection of two systems.
While equinix is perhaps best known for running more than 175 data centers worldwide, our core business is interconnection. Systems approach princeton series in applied mathematics book 41. The work presented in this paper can mainly be divided into two parts i feedback and parallel interconnections and, ii networks. Stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for nonlinear impulsive dynamical. Both allow stability of a feedback interconnection to be verified from the analysis of its components. This book addresses a major problem for todays largescale networked systems. It is proven that dissipativity is equivalent to the existence of a nonnegative storage. The main objective of this paper is to present a unified dissipativity approach for stability analysis of piecewise smooth pws systems with. One of the main results determines global asymptotic stability of the network from the diagonal stability of a dissipativity matrix which incorporates information about the passivity properties of the subsystems, the interconnection structure of the. This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Request pdf nonlinear impulsive dynamical systems part i. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Stability, control and application of timedelay systems. Vector dissipativity theory and stability of feedback interconnections for.
A thorough yet highly readable introduction to the complex world of nonlinear sciencetoday s. In this paper we develop dissipativity theory for discontinuous dynamical systems. Stability properties of interconnected vehicles herbert tanner, vijay kumar and george pappas university of pennsylvania philadelphia, pa, 19104, usa. On structured lyapunov functions and dissipativity in interconnected lti systems abstract. In addition, feedback interconnection partial stability results for nonlinear dynamical systems are developed thereby providing a generalization of the small gain. For the case of l 2 stability, it is compared with other criteria for asymptotic stability, obtained by lyapunov techniques, and. Nonnegative and compartmental dynamical systems by wassim. The stated objective of this book is to develop a unified analysis and control design framework for impulsive and hybrid dynamical systems using a lyapuno impulsive and hybrid dynamcial systems. Stability and feedback interconnections of dissipative impulsive. Constructive nonlinear control universiteitsbibliotheek gent. Several results regarding the dissipativity of systems defined by quadratic differential forms are given, and some open questions are mentioned. Results on stabilization, equivalence to a passive system, inputtostate stability, and passivity of linear delay systems are then provided. Haddad, 9780691127156, available at book depository with free delivery worldwide. This book develops a general stability analysis and control design framework for.
A version of this post was originally published in network world. Each system is assumed to be inputtostate stable iss. A sufficient condition ensuring dissipativity for positive switched systems is given under a designed switching signal. Supplies an introduction to the popular backstepping approach to nonlinear control design gives a thorough discussion of the concept of inputtostate stability includes a discussion of the fundamentals of feedback linearization and related results. For proper operation of the system, it is essential to ensure that after a given disturbance, the system settles down to a new, stable condition. Ydstieb a school of chemical engineering the university of new south wales sydney, nsw, australia b department of chemical engineering carnegie mellon university. The use of inputoutput properties and interconnection matrices for. Read dissipativity and stability of interconnections, international journal of robust and nonlinear control on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Dissipativity of positive switched systems using multiple.
Citeseerx stability of dissipative interconnections. Transient stability analysis is the study of the system in response to these changes and is used to determine if the system will be stable after a given disturbance. Dissipativity theory for nonlinear impulsive dynamical systems. This paper investigates the stability of systems which can be regarded as composed of interconnected subsystems. This work explores lyapunov characterizations of the inputoutputtostate stability ioss property for nonlinear systems. It includes numerical stability tests for delay differential systems and presents. Its been that way since we were founded in 1998 to provide a vendorneutral meeting place where network and internet service providers could connect as they built the early internet. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations. Dissipativity and stability of interconnections willems. Impulsive and hybrid dynamical systems by wassim m.
Wassim michael haddad born july 14, 1961 is a lebanesegreekamerican applied mathematician, scientist, and engineer, with research specialization in the areas of dynamical systems and control. His research has led to fundamental breakthroughs in applied mathematics, thermodynamics, stability theory, robust control, dynamical system theory, and neuroscience. Dissipativity and positivity are shown to be maintained under positive feedback interconnection, and a smallgain property is also given. Inputoutputtostate stability siam journal on control. On structured lyapunov functions and dissipativity in. Partial dissipativity theory and partial stability of feedback. Stability and control of largescale dynamical systems. Stability and control of largescale dynamical systems princeton. Chapter 2 derives a stability test for interconnected systems from the dissipativity characteristics of the subsystems. This is the basis of the classical stability criteria such as the small gain theorem, the positive. Abstract a new definition of dissipativity is proposed. Abstract interconnections of several nonlinear systems with inputs are considered in this paper.
Negative resistance devices are the essence of nonequilibrium behaviors such as switches 8, 17, 22, nonlinear oscillations 19, 23, or chaotic behavior 21, 29. Wassim haddad, winner of the 2014 pendray aerospace. Request pdf dissipative and stability of interconnections a new definition of dissipativity is proposed. However an interconnection of such systems is not stable in general. These results are derived in terms of the theory of dissipative systems. Largescale dynamical systems are strongly interconnected and consist of.
Dissipativity theory for discontinuous dynamical systems. Vector dissipativity theory and stability of feedback interconnections. This assumption can be relaxed into more general dissipativity to show the stability of. Dissipativity and stability analysis using rational. In particular, the restrictions of linearity and unstable subsystems, that appear in previous results, are seen.
Hybrid nonnegative and compartmental dynamical systems 197. Lecture notes in control and information sciences, vol 398. Our goal is to derive a bottomup stability test using dissipativity properties. In chapter 5 we extend the compositional stability analysis tools to performance and safety certi. This book contains a systematic exposition of the elements of. This book, derived from the 4th delsys workshop, contains advances on the theory and applications of timedelay systems with a focus on interconnected systems. This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. In proceedings of the 2012 american control conference, montreal, june 2012, pages paper frc10. Part of the springerbriefs in electrical and computer engineering book series.
Meanwhile, l 1 gain and stability are also get based on dissipativity. General results giving conditions for an interconnected system to be inputoutput andor lyapunov unstable are considered. Such a framework is imperative for modern complex engineering systems that involve interacting continuoustime and discretetime dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of. A decompositionbased approach to stability analysis of largescale stochastic systems. In this paper, we study connections between structured storage or lyapunov functions of a class of interconnected systems dynamical networks and dissipativity properties of the individual systems. Dissipativity and stability of interconnections core. A sufficient condition for inputsoutput l p stability, in terms of the l p gains of the subsystems and their interconnections is derived.
For example, hill and moylan 1977 assumes the q, s, rdissipativity in each subsystem, which is defined by the supply rate s. Supplies an introduction to the popular backstepping approach to nonlinear control design gives a thorough discussion of the concept of inputtostate stability includes a discussion of the fundamentals of feedback linearization and related. This paper focuses on the notions of qsr dissipativity and passivity in hybrid systems. Chapter 2 derives a stability test for interconnected systems from the dissipativity. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. Dissipative and stability of interconnections request pdf.
In contrast, dissipativity theory is a stability the. This enables a very simple formulation of the requirements for instability. It is proven that dissipativity is equivalent to the existence of a non. Such a framework is imperative for modern complex engineering systems that involve. This book develops a general stability analysis and control design framework for nonlinear largescale interconnected dynamical systems, and presents the most complete treatment on vector lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Sergey g nersesov this book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Dissipativity and stability of interconnections citeseerx. It is purely in terms of the rate of supply that goes in and out of a dynamical system. Analysis of interconnected oscillators by dissipativity theory. Networks of dissipative systems eecs at uc berkeley. This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. A considerable part of these works are concerned with practical problems, especially problems from the area of controls and servomechanisms, and concrete problems from engineering, which first gave the decisive impetus for the expansion and modern development of stability theory. Dissipativity and stability of interconnections willems 2007.
429 1587 814 859 486 1418 908 1437 1651 1269 85 1455 1685 310 779 1579 730 1515 737 1340 505 758 480 1016 1250 245 314 86 991 24 310 716 183 939 740 40 831 773