Linear matrix inequality approach to selected problems in analysis, estimation and control of discrete-time systems.

摘要

Linear matrix inequality (LMI) techniques have proved to be valuable and powerful tools in many applications in different fields of science and engineering. Numerous developments on the theory and applications of LMI have been reported in the literature. This has been the trend, especially, since the development of efficient interior-point methods to solve LMIs numerically.; In this dissertation we develop on the applications of LMIs by finding new problems that can be solved using LMI techniques, formulate them into compact and solvable LMIs, provide illustrative examples that can be solved numerically using the available software, and prove that the LMI methods provide efficient solutions which sometimes are advantageous over other approaches and sometimes the only known solution. The focus of this research is mainly on analysis, control, and estimation.; In our treatment of the estimation problem, we consider both constant-parameter and stochastic-parameter systems. In both cases we derive two filters based on keeping either a weighted quadratic function of the estimation error or the energy of a linear function of the estimator error bounded. We formulate the problem of finding the gain of the estimator filter in terms of LMIs that can be solved to find the constant gain. We apply these estimation techniques to such applications as estimating the harmonic signals in power system and estimation of a signal with a random delay in the measurement or uncertain measurement.; In our pursuit of applications in control theory, we consider a variety of analysis and design problems. The types of the systems that we investigate include linear and nonlinear, deterministic and stochastic, time-invariant and state-dependent systems. The problems that we study involve such applications as determining whether a system is stable, investigating detectability and stabilizability and designing observers and state feedback controls, finding the bounds on the state, output energy, and different gains of a system under various conditions, and passivity of a system.; In some of the problems we consider, the LMI approach is an alternative solution to the more traditional approaches. There are other problems we consider, however, which do not have any known analytical solutions and the LMI formulation, with the availability of the numerical methods and the computing power to solve it, appears to be an invaluable technique.