## Qualitative Analysis of Large Scale Dynamical SystemsThis book develops a unified approach to qualitative analysis of large scale systems described by many diversified types of equations. |

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### Contents

1 | |

12 | |

Chapter III Discrete Time Systems and Sampled Data Systems | 91 |

Chapter IV Systems Described by Stochastic Differential Equations | 109 |

Chapter V InfiniteDimensional Systems | 134 |

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### Common terms and phrases

analysis of large apply Banach space bounded with respect boundedness C0-semigroup Chapter choose composite system conic with constants continuous function Corollary decomposition decrescent deﬁned denotes domain dynamical systems eigenvalues exponentially stable extended space feedback systems ﬁnd ﬁnite ﬁrst following result follows from Theorem given in hypothesis Hilbert space inequality inﬁnitesimal interconnected systems interconnecting structure interior conic isolated subsystems large scale systems Lipschitz continuous Lyapunov stability M-matrix margin of boundedness Michel modiﬁed negative deﬁnite nonlinear norm notation ordinary differential equations partial differential equations positive deﬁnite possesses Property proof of Theorem qualitative analysis radially unbounded satisﬁed scalar Lyapunov functions semigroup solution of composite solution of Eq stability results stable with respect stochastic differential equations subsystem 9 successive principal minors system 9 systems described test matrix theory trajectory behavior trivial solution uniformly asymptotically stable uniformly stable vector Lyapunov functions Wiener process