Geir Dullerud

Robust stabilization of sampled-data systems to structured LTI perturbations

Sampled-data systems with stable, structured, LTI (linear time-invariant) perturbations in the half-plane algebra applied to the continuous-time plant are considered. Necessary and sufficient conditions are derived for robust L/sub 2/ stability of such systems. An example is provided to illustrate the results, which shows that the small gain theorem can be an extremely conservative robustness test in this sampled-data context. >

L/sub 1/ analysis and design of sampled-data systems

The focus of this work is L/sub 1/-optimal control of sampled-data systems. A converging approximation procedure is derived to compute the L/sub infinity /-induced norm of closed-loop finite-dimensional linear time-invariant (LTI) sampled-data systems. An approximation method is developed to synthesize L/sub 1/-optimal sampled-data regulators. Finally, an example is provided that illustrates the L/sub 1/ analysis and design techniques presented. >

Model validation for dynamically uncertain systems

Robust control models describe system uncertainty with both unknown additive signals and unknown dynamic perturbations. These unknown but bounded components lead to a model set description. Model validation is the experimental assessment of the ability of this model set to describe the observed system behaviors. In this paper we consider model validation for H∞ compatible models. This paper provides a detailed presentation of the H∞ model validation problem in the discrete frequency, discrete-time, and sampled-data frameworks. In each case the underlying results and the computational algorithms are discussed. The experimental applicability and the computational consequences are discussed in sufficient detail to give the reader an appreciation of the issues surrounding each model/experiment framework.

Guaranteed error bounds for model reduction of linear time-varying systems

Techniques are presented for the model reduction of linear time-varying and linear periodically-varying systems, including the formulation and proof of guaranteed upper bounds for the error. The commonly used method of balanced truncation for linear time-invariant systems is generalized to the time-varying case with explicit error bounds that are derived based on generalizations of the twice-the-sum-of-the-tail formula. The development of these reduction results for time-varying systems relies on a new operator framework for analysis of linear time-varying systems, presented in Dullerad and Lall (1997), in combination with the model reduction methods for uncertain systems developed in Beck et al. (1996).

Robust performance of periodic systems

Robust performance of sampled-data systems to structured periodic and quasi-periodic uncertainty is considered, and necessary and sufficient conditions are derived, The conditions are finite dimensional, and explicitly computing them is investigated; the results are illustrated with an example. This work is readily extended to yield exact and finite dimensional robust performance conditions for structured arbitrary time-varying uncertainty.

Sampled‐data model validation: An algorithm and experimental application

The application of robust control theory requires representative models containing unknown bounded perturbations and unknown bounded noise/disturbance signals. Model validation is a means of assessing the applicability of a given model with respect to experimental data. We consider a sampled-data approach, using a continuous time model, including unknown perturbations and signals, and a discrete experimental datum of finite length. The sampled-data model validation problem can be formulated as a linear matrix inequality problem. A computationally tractable algorithm, which employs data decimation and exploits the problem structure, is presented in the paper. This method is applied to a 2-D heating experiment.

Analysis and synthesis tools for time-varying systems

In this paper new techniques are developed for the analysis of linear time varying (LTV) systems. These lead to a formally simple treatment of problems for LTV systems, allowing methods more usually restricted to time-invariant systems to be employed in the time-varying case. As an illustration of this methodology, the so-called H/sub /spl infin// synthesis problem is solved for linear time-varying systems.

A continuous-time extension condition

This paper presents a continuous-time extension condition which has applications in the areas of identification and model validation of continuous-time systems. Consider two signals, specified on a finite interval. The result gives a necessary and sufficient condition for the existence of a contractive, causal, linear, time-invariant operator, mapping one signal to the other. This result is a continuous time analog of the classical Caratheodory extension theorem.

Necessary and Sufficient Conditions for Robust Stability of SISO Sampled-data Systems to LTI Perturbations

SISO sampled-data systems are considered with stable, additive, LTI perturbations in the half-plane algebra to the continuous-time plant. Necessary and sufficient conditions are derived for robust L2 stability of such sampled-data systems. An example is provided to illustrate the results, and shows that the small gain theorem can be an extremely conservative robustness test in this sampled-data context.

Temporal discretization of spatially distributed systems

There have been efforts previously to use multidimensional system representations for the control of spatially distributed systems. By expressing spatially distributed systems as multidimensional system models, it has been shown that semidefinite programming techniques can be used for control design and analysis. This formulation can in fact be interpreted as the natural generalization of linear fractional transformation based robust control tools to spatially distributed systems. While most models of physical systems are continuous time models, discrete models are required for control implementation. In this paper, we address the issue of constructing discrete time models from continuous time models for spatially distributed systems.