Harry L. Trentelman
University of Groningen
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Featured researches published by Harry L. Trentelman.
IEEE Transactions on Automatic Control | 2002
Harry L. Trentelman; Jan C. Willems
The problem discussed is that of designing a controller for a linear system that renders a quadratic functional nonnegative. Our formulation and solution of this problem is completely representation-free. The system dynamics are specified by a differential behavior, and the performance is specified through a quadratic differential form. We view control as interconnection: a controller constrains a distinguished set of system variables, the control variables. The resulting behavior of the to-be-controlled variables is called the controlled behavior. The constraint that the controller acts through the control variables only can be succinctly expressed by requiring that the controlled behavior should be wedged in between the hidden behavior, obtained by setting the control variables equal to zero, and the plant behavior, obtained by leaving the control variables unconstrained. The main result is a set of necessary and sufficient conditions for the existence of a controlled behavior that meets the performance specifications. The essential requirement is a coupling condition, an inequality that combines the storage functions of the hidden behavior and the orthogonal complement of the plant behavior.
IEEE Transactions on Automatic Control | 2013
Harry L. Trentelman; Kiyotsugu Takaba; Nima Monshizadeh
This paper deals with robust synchronization of uncertain multi-agent networks. Given a network with for each of the agents identical nominal linear dynamics, we allow uncertainty in the form of additive perturbations of the transfer matrices of the nominal dynamics. The perturbations are assumed to be stable and bounded in H∞-norm by some a priori given desired tolerance. We derive state space formulas for observer based dynamic protocols that achieve synchronization for all perturbations bounded by this desired tolerance. It is shown that a protocol achieves robust synchronization if and only if each controller from a related finite set of feedback controllers robustly stabilizes a given, single linear system. Our protocols are expressed in terms of real symmetric solutions of certain algebraic Riccati equations and inequalities, and also involve weighting factors that depend on the eigenvalues of the graph Laplacian. For undirected network graphs we show that within the class of such dynamic protocols, a guaranteed achievable tolerance can be obtained that is proportional to the quotient of the second smallest and the largest eigenvalue of the Laplacian. We also extend our results to additive nonlinear perturbations with L2-gain bounded by a given tolerance.
IEEE Transactions on Automatic Control | 2002
Madhu N. Belur; Harry L. Trentelman
In this paper, we study control by interconnection of linear differential systems. We give necessary and sufficient conditions for. regular implementability of a given linear differential system. We formulate the problems of stabilization and pole placement as problems of finding a suitable, regularly implementable sub-behavior of the manifest plant behavior. The problem formulations and their resolutions are completely representation free, and specified only in terms of the system dynamics. Control is viewed as regular interconnection. A controller is a system that constrains the plant behavior through a distinguished set of variables, namely, the control variables. The issue of implementation of a controller in the feedback configuration and its relation to regularity of interconnection is addressed. Freedom of disturbances in a plant and regular interconnection with a controller also turn out to be inter-related.
Siam Journal on Control and Optimization | 1990
Aa Anton Stoorvogel; Harry L. Trentelman
In this paper the standard
Systems & Control Letters | 2005
A. Agung Julius; Jan C. Willems; Madhu N. Belur; Harry L. Trentelman
H_\infty
Siam Journal on Control and Optimization | 1995
Harry L. Trentelman; Aa Anton Stoorvogel
control problem using state feedback is considered. Given a linear, time-invariant, finite-dimensional system, this problem consists of finding a static state feedback such that the resulting closed-loop transfer matrix has
Mathematics of Control, Signals, and Systems | 1999
Harry L. Trentelman; Paolo Rapisarda
H_\infty
IEEE Transactions on Automatic Control | 1987
Harry L. Trentelman
norm smaller than some a priori given upper bound. In addition it is required that the closed-loop system is internally stable. Conditions for the existence of a suitable state feedback are formulated in terms of a quadratic matrix inequality, reminiscent of the dissipation inequality of singular linear quadratic optimal control. Where the direct feedthrough matrix of the control input is injective, the results presented here specialize to known results in terms of solvability of a certain indefinite algebraic Riccati equation.
IEEE Transactions on Automatic Control | 1999
Harry L. Trentelman; Jan C. Willems
We study the control problem from the point of view of the behavioral systems theory. Two controller constructions, called canonical controllers, are introduced. We prove that for linear time-invariant behaviors, the canonical controllers implement the desired behavior if and only if there exists a controller that implements it. We also investigate the regularity of the canonical controllers, and establish the fact that they are maximally irregular. This means a canonical controller is regular if and only if every other controller that implements the desired behavior is regular.
Siam Journal on Control and Optimization | 2007
C. Praagman; Harry L. Trentelman; R. Zavala Yoé
This paper deals with the sampled-data