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## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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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