Mixed H 2/H ∞ control for linear infinite-dimensional systems

Abstract

In this paper, we consider mixed H2/H∞ control problems for linear infinite-dimensional systems. The first part considers the state feedback control for the H2/H∞ control problems of linear infinite-dimensional systems. The cost horizon can be infinite or finite time. The solutions of the H2/H∞ control problem for linear infinitedimensional systems are presented in terms of the solutions of the coupled operator Riccati equations and coupled differential operator Riccati equations. The second part addresses the observer-based H2/H∞ control of linear infinite-dimensional systems with infinite horizon and finite horizon costs. The solutions for the observer-based H2/H∞ control problem of linear infinite-dimensional systems are represented in terms of the solutions of coupled operator Riccati equations. The first-order partial differential system examples are presented for illustration. In particular, for these examples, the Riccati equations are represented in terms of the coefficients of first-order partial differential systems.