Robust linear filter design via LMIs and controller design with actuator saturation via SOS programming

Robust filtering under different assumptions and formulations are considered. Robust filter design for systems described by time-varying linear fractional transformation (LFT) uncertain models is reformulated as linear matrix inequalities (LMIs) via upper bound techniques. The contribution is the treatment of norm bounded (both structured and unstructured) LFT uncertainty using LMI (rather than Riccati) methods. Furthermore, in the norm bounded unstructured uncertainty case, our results are less conservative than those by methods based on Riccati equations. Robust filter design for systems with time-invariant parameter uncertainties in a polytope is also considered, using parameter dependent Lyapunov functions to solve the problem. In both cases, we use upper bounds rather than the actual performance objectives.; We also exploit that the robust filter design problem (with model uncertainty and noise) is convex in the filter as an operator. The implication is that robust filter design can be carried out directly, rather than minimizing an upper bound of the objective function. We show that finite dimensional approximations can be used to obtain suboptimal solutions with any degree of accuracy. A design algorithm is proposed, which is made up of successive finite dimensional approximations. This algorithm requires a worst case analysis result. A conceptual branch & bound algorithm is outlined, and a practical algorithm is given.; Polynomial state feedback controller synthesis for systems subject to actuator saturation is also considered. We are interested in two kinds of problems. The first one is to design a controller to enlarge a domain of attraction (DOA), and the second is for disturbance rejection. Sum of squares (SOS) programming is the computational tool. These synthesis problems are not convex, and ad-hoc algorithms are proposed. For linear systems with saturation, algorithms here can be used to improve available results.