The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the discrete-time generalised Riccati equation, but, differently from the discrete case, to date the importance of this equation in the context of optimal contro...

In this paper we consider the quadratic optimal control problem of a discrete-time Markovian jump linear system, subject to constrains on the state and control variables. It is desired to find a state feedback controller, which may also depend on the jump variable, that minimizes a quadratic cost and satisfies some upper bounds on the norms of some random variables, related to the state and con...