Periodic Lyapunov equations: some applications and new algorithms

this paper to illustrate this fact are: the optimal periodic LQG control with state feedback and with output feedback, the stabilization with periodic state feedback and the balancing of discrete-time periodic systems. In the last few years there has been a constantly increasing interest for the development of numerical algorithms for the analysis and design of linear periodic discrete-time control systems (Bittanti et al. 1988, Hench and Laub 1994, Sreedhar and Van Dooren 1993). Of particular interest in the above mentioned applications is the efficient and numerically reliable solution of various types of periodic Lyapunov equations. Several possible computational approaches to solve periodic Lyapunov equation are discussed by Sreedhar and Van Dooren (1993). The purpose of this paper is to propose alternative techniques which improve the numerical reliability of existing algorithms