Robustness of Dynamic Systems with Parameter Uncertainties

Robust Control is one of the fastest growing and promising areas of research today. In many practical systems there exist uncertainties which have to be considered in the analysis and design of control systems. In the last decade methods were developed for dealing with dynamic systems with unstructured uncertainties such as HOO_ and £I-optimal control. For systems with parameter uncertainties, the seminal paper of V. L. Kharitonov has triggered a large amount of very promising research. An international workshop dealing with all aspects of robust control was successfully organized by S. P. Bhattacharyya and L. H. Keel in San Antonio, Texas, USA in March 1991. We organized the second international workshop in this area in Ascona, Switzer­ land in April 1992. However, this second workshop was restricted to robust control of dynamic systems with parameter uncertainties with the objective to concentrate on some aspects of robust control. This book contains a collection of papers presented at the International Workshop on Robust Control held at the Centro Stefano Franscini, Monte Verita, Ascona, Switzer­ land on April 12-17, 1992 as well as a list of open problems presented during a dis­ cussion session at the workshop. Thirtyfive leading researchers from all over the world working in the area of robust control of dynamic systems with parameter uncertainties were invited to present their recent results and to discuss with their colleagues the recent advances in this field.

Robust Stability: The Polynomial Case.- Kharitonov’s Theorem and the Second Method of Lyapunov.- Stability Margins of Perturbed Systems.- Frequency Domain Criteria for Robust Root Locations of Generalized Disc Polynomials.- Computation of Value Sets of Uncertain Transfer Functions.- Robust Stability of General Interconnections of Interval Plants and Unstructured Norm Bounded Perturbations.- Algebraic Approach to Checking Strict Positive Real Property of Uncertain Real Rational Functions.- Stability of Convex Hull of Quasipolynomials.- Robust Stability: Multilinear Parameter Dependence.- Robustness Properties of Multilinear Interval Systems.- Easily Testable Sufficient Conditions for the Robust Stability of Systems with Multiaffine Parameter Dependence.- Robustness Analysis for Multilinear Perturbations.- On the Multiaffine Image of a Cube.- Robust Stability: The Nonlinear Case.- Robust Absolute Stability of Continuous Systems.- Robust Stability: The Matrix Case.- A Branch and Bound Method to Check the Stability of a Polytope of Matrices.- Bounds on the Real Stability Radius.- Necessary and Sufficient Conditions for Robust Stability with Structured Time-Invariant Perturbations.- A Nonconservative Kronecker Based Theory for Robust Root Clustering of Linear State Space Models with Real Norm Bounded Uncertainty.- A Necessary and Sufficient Condition for Quadratic Finite Time Feedback Controllability.- Lyapunov Based Robustness.- Lyapunov Functions for Uncertain Systems.- Robustness Analysis of Linear Control Systems with Uncertain Parameters by the Method of Convex Decomposition.- Performance.- H?-Performance of Interval Plants and Interval Feedback Systems.- Linear vs. Nonlinear Approaches to Robustness Analysis of LTI Control Systems.- Control Design.- Analysis andDesign of Robustly Stable Systems via Zero-Set Methods.- A Robust Control Design in the Parameter Space.- Optimizing the Guaranteed Cost in the Control of Uncertain Linear Systems.- Robust PID Control and Lead-Lag Compensation for Linear Interval Systems.- Model Following Robust Control of Linear Time-Varying Uncertain Systems.- A Convex Parameterization of Robustly Stabilizing Controllers.- Robust Compensator Synthesis — An Experimental Application.- Velocity-Independent Yaw Eigenvalues of Four-Wheel Steering Automobiles.- Some Open Problems.