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Uniform asymptotic stability, an initial treatment

Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

in Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter focuses on the uniform asymptotic stability of a closed set. Asymptotic stability is a fundamental property of dynamical systems—one that is usually desired in natural and engineered ... More


Asymptotic stability, an in-depth treatment

Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

in Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter defines local pre-asymptotic stability for a compact (closed and bounded) set and studies its properties for systems that are nominally well-posed or well-posed. While Chapter 3 dealt ... More


Stability Theory via Vector Lyapunov Functions

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter describes a fundamental stability theory for nonlinear dynamical systems using vector Lyapunov functions. It first introduces the notation and definitions before developing stability ... More


Invariance principles

Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

in Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.003.0008
Subject:
Mathematics, Applied Mathematics

This chapter discusses invariance principles, which characterize the sets to which precompact solutions to a dynamical system must converge. They rely on invariance properties of ω‎-limit sets of ... More


Control of Large-Scale Dynamical Systems via Vector Lyapunov Functions

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter introduces the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, showing that asymptotic stabilizability of a nonlinear dynamical system is ... More


Control Vector Lyapunov Functions for Large-Scale Impulsive Systems

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0011
Subject:
Mathematics, Applied Mathematics

This chapter extends the notion of control vector Lyapunov functions to impulsive dynamical systems. Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory to ... More


Large-Scale Impulsive Dynamical Systems

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0010
Subject:
Mathematics, Applied Mathematics

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale ... More


Introduction

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0001
Subject:
Mathematics, Applied Mathematics

This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, with an emphasis on vector Lyapunov function methods and ... More


Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter develops a general framework for finite-time stability analysis based on control vector Lyapunov functions. Specifically, it develops a vector comparison system whose solution is ... More


Coordination Control for Multiagent Interconnected Systems

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter describes a stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems. The framework is applied to the problem of coordination ... More


Large-Scale Continuous-Time Interconnected Dynamical Systems

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter extends classical dissipativity theory to vector dissipativity for addressing large-scale continuous-time interconnected dynamical systems using vector storage functions and vector ... More


Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Wassim M. Haddad and Sergey G. Nersesov

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.001.0001
Subject:
Mathematics, Applied Mathematics

Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social ... More


Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0012
Subject:
Mathematics, Applied Mathematics

This chapter describes sufficient conditions for finite-time stability of nonlinear impulsive dynamical systems. For impulsive dynamical systems, it may be possible to reset the system states to an ... More


Equilibrium

Daniel Friedman, Barry Sinervo, Daniel Friedman, and Barry Sinervo

in Evolutionary Games in Natural, Social, and Virtual Worlds

Published in print:
2016
Published Online:
August 2016
ISBN:
9780199981151
eISBN:
9780190466657
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199981151.003.0004
Subject:
Economics and Finance, Behavioural Economics

Chapter 4 connects the dynamic steady state concepts analyzed in previous chapters to the classic static concepts of Nash equilibrium (NE) and evolutionarily stable state (ESS). It shows that NE is a ... More


Conclusion

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0014
Subject:
Mathematics, Applied Mathematics

This book has described a general stability analysis and control design framework for large-scale dynamical systems, with an emphasis on vector Lyapunov function methods, vector dissipativity theory, ... More


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