Journal ArticleDOI
General Instability Results for Interconnected Systems
David J. Hill,P. Moylan +1 more
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In this paper, general results giving conditions for an interconnected system to be input-output and/or Lyapunov unstable are derived in terms of the theory of dissipative systems, which enables a very simple formulation of the requirements for instability.Abstract:
General results giving conditions for an interconnected system to be input-output and/or Lyapunov unstable are considered. These results are derived in terms of the theory of dissipative systems. This enables a very simple formulation of the requirements for instability. In particular, the restrictions of linearity and unstable subsystems, that appear in previous results, are seen to be unnecessary. Consequently, the relationship between instability and stability conditions is made clearer. A wide variety of useful instability criteria can be easily obtained as special cases.read more
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Journal ArticleDOI
Survey Constructive nonlinear control: a historical perspective
Petar V. Kokotovic,Murat Arcak +1 more
TL;DR: This survey describes the 'activation' of stability, optimality and uncertainty concepts into design tools and constructive procedures in nonlinear control theory and concludes with four representative applications.
Journal ArticleDOI
Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory
TL;DR: In this paper, a Riccati-like matrix equation is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity.
Journal ArticleDOI
Adaptive backstepping controller design using stochastic small-gain theorem
TL;DR: It is shown that the closed-loop system is practically stable in probability and an adaptive output-feedback controller is proposed, combining stochastic small-gain theorem with backstepping design technique.
Proceedings ArticleDOI
Power systems as dynamic networks
David J. Hill,Guanrong Chen +1 more
TL;DR: This paper reviews recent progress in the science of complex networks and suggests fruitful lines of future research into an integrated study of very large (or massive) systems as well as very complex dynamics.
Journal ArticleDOI
Input-to-state-KL-stability and criteria for a class of hybrid dynamical systems
TL;DR: The criteria of IS- KL -stability are established for HDS withIS- KL K 0 -property subsystems via introducing a hybrid dwell time condition, which unifies the often used average dwell-time condition and converse average dwelling time condition.