In particular, when o=0, this yields the definition of a Lyapunov function Finding, for a given supply rate, a valid storage function(or at least proving that one exists)is a major challenge in constructive analysis of nonlinear systems. The most com-

Ch. 13 Difference Equations 1 First-Order Difference Equations Suppose we are given a dynamic equation relating the value y takes on at date t to another variables Wt and to the value y took in the previous period: where o is a constant. Equation(1)is a linear first-order difference equation a difference equation is an expression relating a variable yt to its previous values

Balanced search trees Balanced search tree a search-tree data structure for which a height of o(g n)is guaranteed when implementing a dynamic set of n items

Graphs(review) Definition. a directed graph(digraph G=(, E)is an ordered pair consisting of a set y of vertices(singular: vertex) a sete c× of edges. In an undirected graphG=(V, E), the edge set e consists of unordered pairs of vertices In either case, we have El=O(v2).Moreover if G is connected, then E2v-l, which

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6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology 6.001 Notes: Section 3.1 Slide 3.1.1 This Lecture In this lecture, we are going to put together the basic pieces of Scheme that we introduced in the previous lecture, in order to

6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology 6.001 Notes: Section 5.1 Slide 5.1.1 In this lecture we are going to continue with the theme of building abstractions. Thus far, we have focused entirely on Procedural

6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology 6.001 Notes: Section 7.1 Slide 7.1.1 In the past few lectures, we have seen a series of tools for helping us create procedures to compute a variety of Good programming practices

6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology 6.001 Notes: Section 8.1 Slide 8.1.1 Review: data abstraction In this lecture we are going to introduce a new data type, a data abstraction consists of: specifically to deal with symbols. This may sound a bit odd, but

Department of Electrical Engineering and Computer Science 6.001 Structure and Interpretation of Computer Programs Spring semester, 2005 Project 5- The Meta-Circular Evaluator Issued Monday, April 25 To Be Completed By: Friday, May 6, 6: 00 pm Code to load for this project o Links to the system code files meval. scm, syntax. scm, and environment. scm are provided from the Projects link on the