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Lyapunov function

About: Lyapunov function is a research topic. Over the lifetime, 43012 publications have been published within this topic receiving 906672 citations.


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Journal ArticleDOI
TL;DR: This paper presents control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint, and explores the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions.

1,999 citations

Book
22 Jun 1999
TL;DR: In this article, the authors compare Linear vs. Nonlinear Control of Differential Geometry with Linearization by State Feedback (LSF) by using Linearization and Geometric Non-linear Control (GNC).
Abstract: 1 Linear vs. Nonlinear.- 2 Planar Dynamical Systems.- 3 Mathematical Background.- 4 Input-Output Analysis.- 5 Lyapunov Stability Theory.- 6 Applications of Lyapunov Theory.- 7 Dynamical Systems and Bifurcations.- 8 Basics of Differential Geometry.- 9 Linearization by State Feedback.- 10 Design Examples Using Linearization.- 11 Geometric Nonlinear Control.- 12 Exterior Differential Systems in Control.- 13 New Vistas: Multi-Agent Hybrid Systems.- References.

1,925 citations

Book
27 Sep 2011
TL;DR: In this article, the authors introduce the concept of passive design tools as a design tool for adaptive control and propose a cascade design with feedback passivation of Cascades and partial-state feedback.
Abstract: 1 Introduction -- 1.1 Passivity, Optimality, and Stability -- 1.2 Feedback Passivation -- 1.3 Cascade Designs -- 1.4 Lyapunov Constructions -- 1.5 Recursive Designs -- 1.6 Book Style and Notation -- 2 Passivity Concepts as Design Tools -- 2.1 Dissipativity and Passivity -- 2.2 Interconnections of Passive Systems -- 2.3 Lyapunov Stability and Passivity -- 2.4 Feedback Passivity -- 2.5 Summary -- 2.6 Notes and References -- 3 Stability Margins and Optimality -- 3.1 Stability Margins for Linear Systems -- 3.2 Input Uncertainties -- 3.3 Optimality, Stability, and Passivity -- 3.4 Stability Margins of Optimal Systems -- 3.5 Inverse Optimal Design -- 3.6 Summary -- 3.7 Notes and References -- 4 Cascade Designs -- 4.1 Cascade Systems -- 4.2 Partial-State Feedback Designs -- 4.3 Feedback Passivation of Cascades -- 4.4 Designs for the TORA System -- 4.5 Output Peaking: an Obstacle to Global Stabilization -- 4.6 Summary -- 4.7 Notes and References -- 5 Construction of Lyapunov functions -- 5.1 Composite Lyapunov functions for cascade systems -- 5.2 Lyapunov Construction with a Cross-Term -- 5.3 Relaxed Constructions -- 5.4 Stabilization of Augmented Cascades -- 5.5 Lyapunov functions for adaptive control -- 5.6 Summary -- 5.7 Notes and references -- 6 Recursive designs -- 6.1 Backstepping -- 6.2 Forwarding -- 6.3 Interlaced Systems -- 6.4 Summary and Perspectives -- 6.5 Notes and References -- A Basic geometric concepts -- A.1 Relative Degree -- A.2 Normal Form -- A.3 The Zero Dynamics -- A.4 Right-Invertibility -- A.5 Geometric properties -- B Proofs of Theorems 3.18 and 4.35 -- B.1 Proof of Theorem 3.18 -- B.2 Proof of Theorem 4.35.

1,848 citations

Book
20 Sep 2010
TL;DR: In this article, the authors present a modern theory of analysis, control, and optimization for dynamic networks, including wireless networks with time-varying channels, mobility, and randomly arriving traffic.
Abstract: This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions

1,781 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems and on the basics of hybrid control, focusing on the robustness of asymptotic stability to data perturbation, external disturbances and measurement error.
Abstract: Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.

1,773 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231,526
20223,272
20212,543
20202,791
20192,623
20182,491