Construction and parameterization of all static and dynamic H2-optimal state feedback solutions for discrete-time systems

✍ Scribed by B.M. Chen; A. Saberi; Y. Shamash; P. Sannuti

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 794 KB
• Volume: 30
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(94)90101-5

✦ Synopsis

This paper considers an H2 optimization problem via state feedback for discrete-time systems. The class of problems dealt with here has a left invertible transfer matrix function from the control input to the controlled output. The paper constructs and parameterizes all the static and dynamic HE-optimal state feedback solutions. Moreover, all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed the optimalfixed modes. Every HE-optimal controller must assign among the closed-loop eigenvalues the set of optimal fixed modes. This set of optimal fixed modes includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of pole-zero cancellations present in any HE-optimal design. Most of the results presented here are analogous to, but not quite the same as, those for continuous-time systems. In fact, there are some fundamental differences between the continuous and discrete-time systems reflecting mainly the inherent nature and characteristics of these systems. *