Approximate behaviors

The motivation for this paper is to contribute to a unified approach to modeling, realization, approximation and analysis for systems with a rich class of uncertainty structures. The specific focus is on what is the appropriate framework to model components with uncertainty, and what is the appropriate notion of approximation for such components. Components and systems are conceptualized in terms of their behaviors, which can be specified by parametrized equations. More questions are posed than are answered

Analysis of Implicit Uncertain Systems. Part II: Constant Matrix Problems and Application to Robust H2 Analysis

This paper introduces an implicit framework for the analysis of uncertain systems, of which the general properties were described in Part I. In Part II, the theory is specialized to problems which admit a finite dimensional formulation. A constant matrix version of implicit analysis is presented, leading to a generalization of the structured singular value μ as the stability measure; upper bounds are developed and analyzed in detail. An application of this framework results in a practical method for robust H2 analysis: computing robust performance in the presence of norm-bounded perturbations and white-noise disturbances

Behavioral approach to robustness analysis

This paper introduces a general and powerful framework for modeling and analysis of uncertain systems. One immediate concrete result of this work is a practical method for computing robust performance in the presence of norm-bounded perturbations and both norm-bounded and white-noise disturbances

Robust Quasi-LPV Controller Design via Integral Quadratic Constraint Analysis

Reduced cost of sensors and increased computing power is enabling the development and implementation of control systems that can simultaneously regulate multiple variables and handle conflicting objectives while maintaining stringent performance objectives. To make this a reality, practical analysis and design tools must be developed that allow the designer to trade-off conflicting objectives and guarantee performance in the presence of uncertain system dynamics, an uncertain environment, and over a wide range of operating conditions. As a first step towards this goal, we organize and streamline a promising robust control approach, Robust Linear Parameter Varying control, which integrates three fields of control theory: Integral Quadratic Constraints (IQC) to characterize uncertainty and nonlinearities, Linear Parameter Varying systems (LPV) that formalizes gain-scheduling, and convex optimization to solve the resulting robust control Linear Matrix Inequalities (LMI). To demonstrate the potential of this approach, it was applied to the design of a robust linear parametrically varying controller for an ecosystem with nonlinear predator-prey-hunter dynamics

Application of frequential properties of power systems to robustness analysis

Abstract-This paper studies the application of certain frequency domain properties of a class of power systems to the robustness analysis. The small signal models of a significant class of power systems-namely, systems without resistive losses nor excitation control-was recently shown to meet passivitylike, convex conditions in the frequency domain. A classical benchmark is considered and it is shown that the presence of excitation control and resistive elements does not completely destroy the above-mentioned property, which remains valid in the frequency band associated to the electromechanical modes. The example includes a detailed robustness analysis showing the importance of the a priori knowledge of the frequential properties of these models in the frequency band of interest