CONSTRUCTION AND PARAMETERIZATION OF ALL STATIC AND DYNAMIC H-2-OPTIMAL STATE-FEEDBACK SOLUTIONS FOR DISCRETE-TIME-SYSTEMS

This paper considers an Hz optimization problem via state feedback for discrete-time systems. The class of problems dealt with here has a le ft invertible transfer matrix function from the control input to the c ontrolled output. The paper constructs and parameterizes all the stati c and dynamic H-2-optimal state feedback solutions. Moreover, all the eigenvalues of an optimal closed-loop system are characterized. All op timal closed-loop systems share a set of eigenvalues which are termed the optimal fixed modes. Every H-2-optimal controller must assign amon g the closed-loop eigenvalues the set of optimal fixed modes. This set of optimal fixed modes includes a set of optimal fixed decoupling zer os which shows the minimum absolutely necessary number and locations o f pole-zero cancellations present in any H-2-optimal design. Most of t he results presented here are analogous to, but not quite the same as, those for continuous-time systems. In fact, there are some fundamenta l differences between the continuous and discrete-time systems reflect ing mainly the inherent nature and characteristics of these systems.