A. Megretski

System analysis via integral quadratic constraints

It is demonstrated how a number of widely used tools for stability analysis can be conveniently unified and generalized using integral quadratic constraints (IQCs). The approach has emerged under a combination of influences from the western and Russian traditions of control theory. An IQC based stability theorem is presented, which covers classical small gain conditions with anti-causal multipliers, but gains flexibility by avoiding extended spaces and truncated signals.<<ETX>>

A convex parameterization of robustly stabilizing controllers

This paper treats synthesis of robust controllers for linear time-invariant systems. Uncertain real parameters are assumed to appear linearly in the closed loop characteristic polynomial. The main contribution is to give a convex parameterization of all controllers that simultaneously stabilize the system for all possible parameter combinations. With the new parameterization, certain robust performance problems can be stated in terms of quasi-convex optimization. >

Robustness analysis of periodic systems

Two approaches for robustness analysis of linear periodically time-varying systems are presented. In the first approach the state space matrices of the nominal system are expanded in Fourier series. The system can then be represented as an interconnection of a linear time-invariant system and an uncertainty that contains all harmonic functions in the Fourier series. Integral quadratic constraints (IQCs) can then be used to derive robustness conditions, which are equivalent to several linear matrix inequalities. In the second approach, instead of being factorized out, the harmonic terms are kept in the nominal system. Periodic IQCs are then used to characterize the uncertainties. This generally gives a lower dimensional optimization problem but with added complexity due to the fact that the system matrices are periodic.

Robustness of periodic trajectories

Robustness analysis of periodic trajectories is discussed in the paper. Conditions for existence and stability of periodic solutions to uncertain non-autonomous systems is obtained from a linearization of the system along an uncertain trajectory. Furthermore, a bound on the distance between the perturbed and the nominal trajectory is verified using a sensitivity derivative.

On l ∞ robust stability and performance with l 2 and l ∞ perturbations ubscrpt> perturbations

In this paper we will consider systems with linear time-invariant perturbations. We will analyze robust performance in the l2 and l∞ settings. The l2 setting gives rise to the familiar case of structured singular values, and a stability criterion is given by the “small μ” theorem. We show that although the necessary and sufficient criterion of robust stability for the l∞ case (l∞ stability with structured l∞-gain bounded perturbations) is the same “small μ” criterion, a system with l2-gain bounded perturbations is never l∞ stable.

Quadratically constrained linear-quadratic optimization of linear output feedback: a linear matrix inequalities approach

In this paper, it is shown how a special nonconvex constrained optimization problem-the linear-quadratic optimal output feedback control problem with finite number of quadratic constraints-can be reduced to minimization of a linear functional on a set of all solutions of a system of linear matrix inequalities. The proposed approach simplifies the existing frequency-domain techniques for solving this problem, and can be effectively used in loopshaping procedures.