Analysis, estimation and controller design of parameter-dependent systems using convex optimization based on linear matrix inequalities

In this thesis, we outline three contributions in robust control. The first is the efficient computation of a lower bound on the robust stability margin (RSM) of uncertain systems. A lower bound on the RSM can be derived using the framework of integral quadratic constraints (IQCs). Current techniques for numerically computing this lower bound use a bisection scheme. We show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem, which can be solved very efficiently using standard algorithms. For the second contribution, we focus on linear systems affected by parametric uncertainties. For these systems, we present sufficient conditions for robust stability. We also derive conditions for the existence of a robustly stabilizing gain-scheduled controller when the system has time-varying parametric uncertainties that can be measured in real time. Our approach is proven to be in general less conservative than existing methods. Our third contribution is on the robust estimation of systems having parametric uncertainties. For systems with mixed deterministic and stochastic uncertainties, we design two optimized steady state filters: (i) the first filter minimizes an upper bound on the worst-case gain in the mean energy between the noise affecting the system and the estimation error; (ii) the second filter minimizes an upper bound on the worst-case asymptotic mean square estimation error when the plant is driven by a white noise process. For time-varying systems with stochastic uncertainties, we derive a robust adaptive Kalman filtering algorithm. This algorithm offers considerable improvement in performance when compared to the standard Kalman filtering techniques. We demonstrate the performance of these robust filters on numerical examples consisting of the design of equalizers for communication channels