STATE COVARIANCE ASSIGNMENT OF DISCRETE SYSTEMS: DEVELOPMENT AND APPLICATIONS

Performance objectives that are expressed as upper bounds on the steady state variances of the system outputs and inputs are quite common in stochastic control problems. Past approaches to developing control laws for constrained variance objectives have been indirect. Currently, the most direct approaches are those based on linear-quadratic (LQ) theory which allow the designer to synthesize a controller which minimizes a weighted sum of the input and output variances. Since minimizing a scalar cost does not insure that the multiple variance requirements will be satisfied, iterative schemes must be used to determine the weights in the LQ cost functional. The LQ approaches at present have two deficiencies. First of all, it has not been proved that weights exist which will satisfy the variance requirements even if a satisfying controller is known to exist apriori. Also, the iterative schemes which have been developed to search for the weights are not proven to converge. Now it is possible to meet the output variance requirements by assigning a specified state covariance to the system. Thus, this dissertation introduces and solves the following (state covariance assignment) problem for linear discrete-time systems: (i) characterize the entire set of state covariances which may be assigned to a system by state feedback and (ii) find the set of all state feedback gains which will assign an admissible state covariance to the system