The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Criteria for robust stability and stabilization of uncertain linear systems with state delay

This paper deals with the problem of robust stabilization for uncertain systems with multiple state delays. The parameter uncertainties are time-varying and unknown but are norm-bounded, and the delays are time-varying. A new method for achieving robust stabilization is presented for a class of uncertain time-delay systems via linear memoryless state feedback control. The results depend on the size of the delays and are given in terms of several linear matrix inequalities.

Delay-dependent robust stabilization of uncertain systems with multiple state delays

The power grid is not only a network interconnecting generators and loads through a transmission and distribution system, but is overlaid with a communication and control system that enables economic and secure operation. This multilayered infrastructure has evolved over many decades utilizing new technologies as they have appeared. This evolution has been slow and incremental, as the operation of the power system consisting of vertically integrated utilities has, until recently, changed very little. The monitoring of the grid is still done by a hierarchical design with polling for data at scanning rates in seconds that reflects the conceptual design of the 1960s. This design was adequate for vertically integrated utilities with limited feedback and wide-area controls; however, the thesis of this paper is that the changing environment, in both policy and technology, requires a new look at the operation of the power grid and a complete redesign of the control, communication and computation infrastructure. We provide several example novel control and communication regimes for such a new infrastructure.

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Designing the Next Generation of Real-Time Control, Communication, and Computations for Large Power Systems

Load frequency control has been used for decades in power systems. Traditionally, this has been a centralized control by area with communication over a dedicated and closed network. New regulatory guidelines allow for competitive markets to supply this load frequency control. In order to allow an effective market operation, an open communication infrastructure is needed to support an increasing complex system of controls. While such a system has great advantage in terms of cost and reliability, the possibility of communication signal delays and other problems must be carefully analyzed. This paper presents a load frequency control method based on linear matrix inequalities. The primary aim is to find a robust controller that can ensure good performance despite indeterminate delays and other problems in the communication network.

Application of linear matrix inequalities for load frequency control with communication delays

A stability criterion for linear time-delay systems described by a differential difference equation of the form dx(t)=Ax(t)+Bx(t- tau ) is proposed. The result obtained includes information on the size of the delay and therefore can be a delay-dependent stability condition. Its relation to existing delay-independent stability criteria is also discussed. >

Stability of x(t)=Ax(t)+Bx(t- tau )

The problem of finding the conditions under which an interval polynomial has a given number of roots in the open left-half plane and the other roots in the open right-half plane, irrespective of the values of its coefficients, is considered. A simple criterion is provided to test interval polynomials for the root distribution invariance, viewed as an extension of Kharitonov's theorem. The goal is to provide an alternative theorem and then give an efficient means of checking the root distribution invariance. >

A root distribution criterion for interval polynomials

It is pointed out that in order to check the quadratic stability of a family of linear systems with a stable nominal system, the positive definiteness constraint can be dropped from the quadratic Lyapunov function. >

H. Kokame

Papers

Stability of x(t)=Ax(t)+Bx(t- tau )

A root distribution criterion for interval polynomials

An exact quadratic stability condition of uncertain linear systems