*Wassim M. Haddad and Sergey G. Nersesov*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691153469
- eISBN:
- 9781400842667
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153469.003.0008
- Subject:
- Mathematics, Applied Mathematics

This chapter develops vector dissipativity notions for large-scale nonlinear discrete-time dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale ...
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This chapter develops vector dissipativity notions for large-scale nonlinear discrete-time dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear discrete-time dynamical systems in terms of a vector dissipation inequality involving a vector supply rate, a vector storage function, and a nonnegative, semistable dissipation matrix. On the subsystem level, the proposed approach provides a discrete energy flow balance in terms of the stored subsystem energy, the supplied subsystem energy, the subsystem energy gained from all other subsystems independent of the subsystem coupling strengths, and the subsystem energy dissipated. The chapter also develops extended Kalman–Yakubovich–Popov conditions, in terms of the local subsystem dynamics and the interconnection constraints, for characterizing vector dissipativeness via vector storage functions for large-scale discrete-time dynamical systems.Less

This chapter develops vector dissipativity notions for large-scale nonlinear discrete-time dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear discrete-time dynamical systems in terms of a vector dissipation inequality involving a vector supply rate, a vector storage function, and a nonnegative, semistable dissipation matrix. On the subsystem level, the proposed approach provides a discrete energy flow balance in terms of the stored subsystem energy, the supplied subsystem energy, the subsystem energy gained from all other subsystems independent of the subsystem coupling strengths, and the subsystem energy dissipated. The chapter also develops extended Kalman–Yakubovich–Popov conditions, in terms of the local subsystem dynamics and the interconnection constraints, for characterizing vector dissipativeness via vector storage functions for large-scale discrete-time dynamical systems.

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

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153896
- eISBN:
- 9781400842636
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153896.003.0001
- Subject:
- Mathematics, Applied Mathematics

This chapter presents the model of a hybrid system to be used in this volume. The focus is on the data structure and on modeling. The model suggests that the flow set, the flow map, the jump set, and ...
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This chapter presents the model of a hybrid system to be used in this volume. The focus is on the data structure and on modeling. The model suggests that the flow set, the flow map, the jump set, and the jump map can be specialized to capture the dynamics of purely continuous-time or discrete-time systems on ℝn. The former corresponds to a flow set equal to ℝn and an empty jump set, while the latter can be captured with an empty flow set and a jump set defined as ℝn. In addition, several examples of hybrid systems are given, including models of hybrid control systems. The model of a hybrid system is then related to other modeling frameworks; such as hybrid automata, impulsive differential equations, and switching systems.Less

This chapter presents the model of a hybrid system to be used in this volume. The focus is on the data structure and on modeling. The model suggests that the flow set, the flow map, the jump set, and the jump map can be specialized to capture the dynamics of purely continuous-time or discrete-time systems on ℝ^{n}. The former corresponds to a flow set equal to ℝ^{n} and an empty jump set, while the latter can be captured with an empty flow set and a jump set defined as ℝ^{n}. In addition, several examples of hybrid systems are given, including models of hybrid control systems. The model of a hybrid system is then related to other modeling frameworks; such as hybrid automata, impulsive differential equations, and switching systems.

*Stevan Berber*

- Published in print:
- 2021
- Published Online:
- September 2021
- ISBN:
- 9780198860792
- eISBN:
- 9780191893018
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198860792.003.0014
- Subject:
- Physics, Atomic, Laser, and Optical Physics, Condensed Matter Physics / Materials

Due to the importance of the concept of independent discrete variable modification and the definition of discrete linear-time-invariant systems, Chapter 14 presents and discusses basic deterministic ...
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Due to the importance of the concept of independent discrete variable modification and the definition of discrete linear-time-invariant systems, Chapter 14 presents and discusses basic deterministic discrete-time signals and systems. These discrete signals, which are expressed in the form of functions, including the Kronecker delta function and the discrete rectangular pulse, are used throughout the book for deterministic discrete signal analysis. The chapter also presents the definition of the autocorrelation function and the explanation of the convolution procedure in linear-time-invariant systems for discrete-time signals in detail, due to the importance of these in the analysis and synthesis of discrete communication systems.Less

Due to the importance of the concept of independent discrete variable modification and the definition of discrete linear-time-invariant systems, Chapter 14 presents and discusses basic deterministic discrete-time signals and systems. These discrete signals, which are expressed in the form of functions, including the Kronecker delta function and the discrete rectangular pulse, are used throughout the book for deterministic discrete signal analysis. The chapter also presents the definition of the autocorrelation function and the explanation of the convolution procedure in linear-time-invariant systems for discrete-time signals in detail, due to the importance of these in the analysis and synthesis of discrete communication systems.