Sampled-Data H2 Control for Symmetric Systems

Abstract

This paper considers digital control problems for continuous-time systems having symmetric transfer functions. It is supposed that digital controllers are implemented with zero-order hold, discrete-time controller, and ideal or integral sampler. The following results are obtained : (1) stabilization : transfer functions of discretized systems with both types of samplers keep symmetries of original continuous-time transfer functions. A condition for discrete-time stabilizing controllers to be symmetric is obtained. (2) discrete-time H2 control synthesis : discrete-time H2 optimal controllers for symmetric discrete-time generalized plants are symmetric. (3) sampled-data H2 control synthesis : for symmetric continuous-time generalized plants with integral samplers, sampled-data H2 optimal controllers are symmetric, while symmetries can not be utilized with ideal samplers.