A. S. Morse

Basic problems in stability and design of switched systems

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Systematic design of adaptive controllers for feedback linearizable systems

A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed. The coordinate-free geometric conditions, which characterize this class of systems, do not constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called parametric-pure feedback form. When this form is strict, the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results use simple analytical tools, familiar to most control engineers. >

Decoupling and Pole Assignment in Linear Multivariable Systems: A Geometric Approach

Decoupling and pole assignments in linear multivariable control systems using geometric method

A Theory of Network Localization

In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly

Rigidity, computation, and randomization in network localization

We provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.

Structural Invariants of Linear Multivariable Systems

This article identifies some of the structural properties of the matrix triple

Status of noninteracting control

(C,A,B)

A toolkit for nonlinear feedback design

which remain invariant under various transformation groups. The paper begins with a brief account of a recent result which states that the controllable space of

Adaptive stabilization of linear systems with unknown high-frequency gains

(A,B)

Network localization in partially localizable networks

can be decomposed into a direct sum of singly-generated controllability subspaces, the dimension of each subspace being determined by one of the controllability indices of