### Optimization and Systems Theory Seminar

Tuesday, December 8, 1998, 11.00-12.00, Room 3721, Lindstedtsvägen 25

** Dr. Ulf Jönsson**

Laboratory for Information and Decision Systems

Massachusetts Institute of Technology

Cambridge, Massachusetts, USA

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Computations in robustness analysis

A useful idea in systems analysis is to divide the system into a
nominal part and a perturbation. Attractive conditions for robust
stability and robust performance can then be obtained if the nominal
part is suitable for computations. The idea is to use
Integral Quadratic Constraints (IQCs) to characterize the perturbation
and then solve a convex optimization problem defined in terms of the IQCs.

In the first part of the talk we discuss the basic ideas behind the
IQC methodology and the computational problems it gives rise to. For
this part of the talk we assume that the nominal system is linear time
invariant and that the IQCs are used to characterize unmodeled
dynamics, uncertainties, nonlinearities, signals, and other system
components.

In the second part of the talk we discuss new research on robustness
analysis of periodic trajectories. The IQC methods from the first part
of the talk are extended to compute robustness margins of nonlinear
systems that exhibit a stable periodic solution due to external periodic
forcing. This problem has applications in, for example, control
problems where the nominal controller is designed to give good
tracking and we want to consider robustness with respect to structured
dynamic uncertainty in the system.

Our analysis gives rise to a robustness problem for systems with periodic
nominal dynamics. We address this problem with an IQC method
that results in an infinite dimensional convex optimization problem. An
algorithm based on a frequency theorem for periodic systems by Yakubovich
is used to solve the optimization problem.

The second part of the talk is joint work with Alexandre Megretski and
Chung-Yao Kao.

Calendar of seminars

*Last update: December 3, 1998 by
Anders Forsgren,
andersf@math.kth.se.
*