Abstract not found

Conventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree topology restriction precludes the use of these methods in several sizing problems of significant importance to high-performance deep submicron design including, for example, circuits with loops of resistors, e.g., clock distribution meshes, and circuits with coupling capacitors, e.g., buses with crosstalk between the lines. The paper proposes a new optimization method which can be used to address these problems. The method uses the dominant time constant as a measure of signal propagation delay in an RC circuit, instead of Elmore delay. Using this measure, sizing of any RC circuit can be cast as a convex optimization problem which can be solved using the recently developed efficient interi...

In this paper we address the problem of low-authority controller (LAC) design. The premise is that the actuators have limited authority, and hence cannot significantly shift the eigenvalues of the system. As a result, the closed-loop eigenvalues can be well approximated analytically using perturbation theory. These analytical approximations may suffice to predict the behavior of the closed-loop system in practical cases, and will provide at least a very strong rationale for the first step in the design iteration loop. We will show that LAC design can be cast as convex optimization problems that can be solved efficiently in practice using interior-point methods. Also, we will show that by optimizing the ℓ1 norm of the feedback gains, we can arrive at sparse designs, i.e., designs in which only a small number of the control gains are nonzero. Thus, in effect, we can also solve actuator/sensor placement or controller architecture design problems. Keywords: Low-authority control, actuator/sensor placement, linear operator perturbation theory, convex optimization, second-order cone programming, semi-definite programming, linear matrix inequality. 1

We consider analysis and controller synthesis of piecewise-linear systems. The method is based on constructing quadratic and piecewise-quadratic Lyapunov functions that prove stability and performance for the system. It is shown that proving stability and performance, or designing (state-feedback) controllers, can be cast as convex optimization problems involving linear matrix inequalities that can be solved very e ciently. A couple of simple examples are included to demonstrate applications of the methods described. Key words: Piecewise-linear systems, quadratic stabilization, linear matrix inequality (LMI). 1

We present a new semidefinite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities (LMIs), and hence they can be easily handled by recent interior-point methods. Using this LMI formulation, we can cast several interesting filter design problems as convex or quasi-convex optimization problems, e.g., minimizing the length of the FIR filter and computing the Chebychev approximation of a desired power spectrum or a desired frequency response magnitude on a logarithmic scale.

Since 1984 there has been a concentrated e ort to develop e cient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interior-point methods (beyond their e ciency for LP): they extend gracefully to nonlinear convex optimization problems. New interior-point algorithms for problem classes such as semide nite programming (SDP) or second-order cone programming (SOCP) are now approaching the extreme e ciency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to e ciently solve nonlinear convex optimization problems opens up new applications. In the rst example we show how SOCP can be used to solve robust open-loop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the set-point and feedback gains for a controller, and compare this method with the more standard approach. Our nal application concerns analysis and synthesis via linear matrix inequalities and SDP. Submitted to a special issue of Journal of Process Control, edited by Y. Arkun & S. Shah, for papers presented at the 1997 IFAC Conference onAdvanced Process Control, June 1997, Ban. This and related papers available via anonymous FTP at

This paper presents a new, iterative algorithm for designing full order LTI controllers for systems with real parameter uncertainty. Robust stability isdetermined for these systems using the Popov analysis criterion and multiplier, and robust performance is investigated using a bound on the output energy. Control design to minimize the robust performance metric naturally leads to Bilinear Matrix Inequalities, which can be decoupled to a large extent. However, coupling remains in the problem since we simultaneously optimize the parameters of both the Popov stabilitymultiplier and the compensator. We present a heuristic, iterative algorithm to solve this design problem, and demonstrate that it works effectively on two numerical examples. In the process, we illustrate that the key advantages of this control design approach are the high reliability of the numerical techniques and the relative simplicity of implementing the algorithm. 1

This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 performance synthesis problem, is shown to be applicable to the robust controller design with the H1 cost. Although the performance metrics are di erent, we demonstrate that the same solution algorithm based on LMI synthesis leads to a very effective and e cient technique for real parametric robust H1 control design. Furthermore, it is di cult to compare robust H2 controllers to =Km designs, but in this work we provide insights into the issue of conservatism for various robust H1 control approaches, in particular, the Popov controller synthesis, the robust H1 design, and the =Km synthesis. The detailed analysis of these approaches is demonstrated on a exible structure benchmark problem. Keywords: Lur'e system, real parametric uncertainty; L2 gain; Popov controller synthesis; bilinear matrix inequality; linear matrix inequality. 1

This work builds on the stability analysis of piecewisea #ne systems reported in #1# and extends it to obtain a new synthesis tool for output feedback controllers. The proposed technique relies on formulating the search for a piecewisequadratic Lyapunov function and a piecewise-a#ne controller as a Bilinear Matrix Inequality. This can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities which can be solved numerically very e#ciently. Akey point in this design technique is that it can be used to design controllers with di#erent structures depending on the number of constraints that are added. In particular, it is shown that a controller with the structure of a regulator and estimator can be designed so that switching based on state estimates rather than on the output can be performed. It is also shown that many other desired features can be included in the design, such as boundedness of the control signals. Furthermore, the applicabilit...

We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1.1) where the matrices Fi = F T