Robust Control Of Uncertain Stochastic Systems

Stochastic control, especially for the systems governed by Ito-type stochastic differential equations, has become a popular research field of modern control theory due to its great many applications in signal processing, mathematical finance and population modeling.At the first, the basic concept and content of linear matrix inequality are expounded, and the algorithms and software for solving LMI problems are introduced. An example in the stochastic uncertain control theory is given to illustrate LMI applications. It is shown that a number of important problems from the stochastic control theory can be reformulated as convex optimization problems with linear matrix inequality (LMI) constraints, so that they will become numerically tractable.Second, this paper discusses the robust H_∞filtering of stochastic uncertain linear systems. We assume the uncertain matrix is norm bounded and time-varying, while the external disturbance is a stochastic process. By means of linear matrix inequality the H_∞filtering was constructed, and an example was presented to illustrate the developed theory.Third, this paper is to study the discrete-time stochastic H₂ /H_∞control with state and external disturbance and control input dependent noise. A necessary and sufficient condition for existence of H₂ /H_∞control is presented, which transforms the H₂ /H_∞controller design into solving four coupled matrix-valued equations. An example was presented to illustrate what we have presented in this paper have the advantage of easy computation.Finally, this paper discusses the quadratic stabilization and quadratic guaranteed cost control for stochastic uncertain systems, where the uncertain matrix is norm bounded. First, a necessary and sufficient condition for the quadratic stabilization of stochastic uncertain systems is given via linear matrix inequalities; second, we give the definition of quadratic guaranteed cost control of uncertain stochastic systems, and prove that the state feedback law u (t )= Kx(t) can enable the system to achieve quadratic stability and the cost function is bounded via the linear matrix inequality. We give relationship between quadratic guaranteed cost control and stabilizable.