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

this paper concerns a linear system whose state-space equations depend rationally on real, time-varying parameters, which are measured in real time. A stabilizing, parameter-dependent controller is sought, such that a given L

this article is to provide an overview of the state of the art of

Integral quadratic constraints (IQCs) can be used for proving stability of systems with uncertainties and nonlinearities. Similarly, IQCs can also be used for controller synthesis. Necessary and sufficient conditions for the existence of such a controller is derived. These conditions include linear matrix inequalities (LMIs) and matrix inertia specifying the number of negative eigenvalues of a matrix. In general, these conditions are nonconvex. Connections to bilinear matrix inequalities and LMIs with rank constraints are also given. Keywords: controller synthesis, matrix inertia, linear matrix inequalities, integral quadratic constraints. 1 Introduction Linear matrix inequalities (LMIs) have been used during the last ten years for analysis and synthesis of robust control systems. The reason for this emerging interest is twofold. First, analysis and synthesis problems can be formulated as LMIs. Secondly, efficient numerical solvers have been developed and are now available. One impor...

This paper copes with the problem of satisfying input and/or state hard constraints in set-point tracking problems. Stability is guaranteed by synthesizing a Lyapunov quadratic function for the system, and by imposing that the terminal state lies within a level set of the function. Procedures to maximize the volume of such an ellipsoidal set are provided, and interior-point methods to solve on-line optimization are considered. Key words: Predictive control, Constraints, Lyapunov function, Set-point control, Optimization problems, Interior-point methods, Quadratically constrained quadratic programming. 1 Introduction The necessity of satisfying input/state constraints is a feature that frequently arises in control applications. Constraints are dictated for instance by physical limitations of the actuators or by the necessity to keep some plant variables within safe limits. In recent years, several control techniques have been developed which are able to handle hard constraints, see e....