Tarraf, Danielle C., Megretski, Alexandre, Dahleh, Munther A.
This paper develops a constructive approach for designing finite state controllers to stabilize pairs of unstable, homogeneous second order discrete-time systems with binary sensor measurements: The...
Input Classes for Identification of Bilinear Systems (2009)
Eduardo D. Sontag, Yuan Wang, Alexandre Megretski
This paper asks what classes of input signals are sufficient in order to completely identify the input/output behavior of generic bilinear systems. The main results are that step inputs are not...
Library of Congress Cataloging-in-Publication Data (2008)
Vincent D. Blondel, Alexandre Megretski, Edited Vincent, D. Blondel, Poul Anderson
Unsolved problems in mathematical systems and control theory
A Framework for Robust Stability of Systems Over Finite Alphabets (2008)
Tarraf, Danielle C., Megretski, Alexandre, Dahleh, Munther A.
Systems over finite alphabets are discrete-time systems whose input and output signals take their values in finite sets. Three notions of input/output stability (gain stability, incremental stability...
On the Gap Between Structured Singular Values and Their Upper Bounds (2007)
A geometric description of the gap between complex structured singular value (SSV or ) and its "D-scaling" upper bound is given. As an application, it is shown that the gap grows not faster...
Controller Design for a Class of Underactuated Nonlinear Systems (2007)
Reza Olfati-saber, Alexandre Megretski
In this paper, we design a controller for a class of underactuated nonlinear systems. First, we try to find an appropriate global change of coordinates to transform the dynamics of the system into a...
Robustness of Finite State Automata (2007)
Alexandre Megretski Mit, Alexandre Megretski
The classical robust control deals with systems which can be approximated by nite order linear time-invariant (LTI) models, uses integral constraints, such as induced gain bounds, to assess...
Input Classes for Identification of Bilinear Systems (2006)
Sontag, Eduardo D., Wang, Yuan, Megretski, Alexandre
This paper asks what classes of input signals are sufficient in order to completely identify the input/output behavior of generic bilinear systems. The main results are that step inputs are not...
Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions (2003)
Gonçalves, Jorge M., Megretski, Alexandre, Dahleh, Munther A.
This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS...
Positivity of Trigonometric Polynomials (2003)
The paper introduces a modi cation of the well-known sum-ofsquares relaxation scheme for semi-algebraic programming by Shor [1], based on replacing the ordinary polynomials by their trigonometric...
Optimal Detection of Symmetric Mixed Quantum States (2002)
Eldar, Yonina C., Megretski, Alexandre, Verghese, George C.
We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of...
Designing Optimal Quantum Detectors Via Semidefinite Programming (2002)
Eldar, Yonina C., Megretski, Alexandre, Verghese, George C.
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of...
Relaxations of Quadratic Programs (2001)
In Operator Theory, Alexandre Megretski
The paper describes a class of mathematical problems at an intersection of operator theory and combinatorics, and discusses their application in complex system analysis. The main object of study is...
Relaxation of Quadratic Programs in Operator Theory and System Analysis (2001)
Abstract. The paper describes a class of mathematical problems at an intersection of operator theory and combinatorics, and discusses their application in complex system analysis. The main object of...
Analysis of Essentially Nonlinear Systems (1998)
The objective of the research supported by AFOSR was development of new techniques for rigorous and efficient computer-aided analysis and design of essentially nonlinear systems. Applications of...
New Tools in Nonlinear System Analysis (1998)
This project was aimed at developing novel theories for the analysis and design of systems exhibiting essentially nonlinear behavior, such as systems utilizing quantized decision making, periodic...
Robustness Analysis and Synthesis for Essentially Nonlinear Systems (1998)
The research was concentrated on developing an advanced theory of stability and performance analysis of nonlinear dynamical systems. The ultimate goal is to provide algorithms and software for...
Controller design for the beam-and-ball System (1998)
Reza Olfati-saber, Alexandre Megretski
We design a controller for the Beam-and-Ball system that renders the origin semiglobally asymptotically stable (semi-GAS). First, we view the problem as designing a controller for a second-order...
A Guide To IQCbeta: Software For Robustness Analysis (1998)
Alexandre Megretski, Chung-Yao Kao, Ulf Jönsson, Anders Rantzer
Contents 1 Getting Started 4 1.1 About IQCfi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Installation of IQCfi . . . . . . . . . . . . . . . . . . . . . . . ....