PPT-Lyapunov

Functions and Memory Justin Chumbley Why do we need more than linear analysis What is Lyapunov theory Its components What does it bring Application episodic learningmemory Linearized stability of nonlinear systems Failures. These tools will be used in the next section to analyze the stability properties of a robot controller We present a survey of the results that we shall need in the sequel with no proofs The interested reader should consult a standard text such as Vi Jim Zhu Yong Liu and Rui Hang Abstract This paper presents the formulation of a Lyapunov function for an exponentially stable linear time varying LTV system using a welldefined PDspectrum and the associated PDeigenvectors It provides a bridge betwee Institut Desargues Universit57524e de Lyon 1 69622 Villeurbanne France clarkeigdunivlyon1fr Summary The method of Lyapunov functions plays a central role in the study of the controllability and stabilizability of control systems For nonlinear system In this chapter were going to learn one reason why some systems go to an equilibrium For example the pure coordination game goes to an equilibrium Markets go to equilibrium Other models such as Conways Game of Life do not go to equilibrium They prod 73, NUMBER 14 PH YSICAL REVIEW LETTERS 3 OcTQBER 1994 one-step error &n is a first-order approximation to this constant that is explicitly computable. The test brittleness is determined from the Jacob Lectures: Each . Tuesday at . 16:00. . (First lecture: . May 21, . last lecture: . June 25. ). Thomas . Kreuz. , ISC, . CNR. . thomas.kreuz@cnr.it. . http://www.fi.isc.cnr.it/users/thomas.kreuz. s. tructure: stability analysis of contact dynamics via sums-of-squares. Michael Posa. Joint work with Mark . Tobenkin. and Russ Tedrake. Massachusetts Institute of Technology. BIRS Workshop on Computational Contact Mechanics. Manoj Gopalkrishnan. TIFR Mumbai. manoj.gopalkrishnan@gmail.com. Here is a Markov chain. 1. 2. 3. Here is a reaction network. Continuous-time discrete-space Markov chain = . Unimolecular. reaction network. Lagrangian. Coherent Structures from. Lyapunov. Exponents. TopoInVis. 2011. Filip. . Sadlo. , Markus . Üffinger. , Thomas Ertl, Daniel . Weiskopf. VISUS - University of Stuttgart. Different Finite-Time Scopes. Radko . Kříž. University of Hradec Kralove. Faculty of Science. Radko.kriz@uhk.cz. . Content. Introduction. Input data. Methodology. Results. Conclusions. Introduction. Is the world stochastic or deterministic. Design and Analysis of Hybrid Systems. Spring 2018. CS 599.. Instructor: Jyo Deshmukh. Acknowledgment: Some of the material in these slides is based on the lecture slides for CIS 540: Principles of Embedded Computation taught by Rajeev Alur at the University of Pennsylvania. . Basics of Control. Spring 2018. CS 599.. Instructor: Jyo Deshmukh. Acknowledgment: Some of the material in these slides is based on the lecture slides for CIS 540: Principles of Embedded Computation taught by Rajeev Alur at the University of Pennsylvania. http://www.seas.upenn.edu/~cis540/. in. Industrial Practice. Jyotirmoy V. Deshmukh. Xiaoqing. Jin. Jim Kapinski. Hisahiro Ito. Ken Butts. Alexandre. . Donzé. Sanjit. A. . Seshia. . Joint work with. :. TexPoint fonts used in EMF. . A unifying and intuitive approach to . linking static and dynamic stability. Dai . Zusai. Philadelphia, U.S.A.. Lyapunov function. i. ) . attains the minimum value only at an equilibrium; .  . ii) .