Robust Analysis And Design For Uncertain Systems Based On The Convex Theory

Linear Matrix Inequality (LMI) is one powerful tool for different aspects of studies in the control field. Many problems, which include robust identification, model validation and robust controller analysis and synthesis etc, can all be reduced to the resolve of linear matrix inequality or inequalities. With the underwater vehicle as the object for study, based on the research results about LMI, this dissertation presents some research work on the problems mentioned above. The main contributions present as follows: 1. Studied robust identification and model validation on the basis of convex theory. The problems studied are based on mixed time-domain/frequency-domain input-output data. Related algorithms via convex optimization are given. 2. Discussed analysis and synthesis techniques for robust pole placement in LMI regions. Focused on linear systems with static uncertainty on the state matrix, the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The analysis results are then applied to the synthesis of dynamic output feedback controllers. 3. Present the design method of state- or output- feedback H2 /H~, controllers with regional pole placement constraints. Sufficient and necessary condition for feasibility is derived for a general class of convex regions of the complex plane. The validity and applicability of the approach are illustrated by 2 simple examples. 4. Selected the ordinate navigation system of certain underwater vehicle as applied object, used Matlab LMI Toolbox as the main computation tool, designed state- and output- feedback controllers mixed H2 /H,, performance requirement with regional pole placement constraints. The simulation results preliminarily show that the robust performance is satisfied.