LQ control of behavior systems in kernel representation

In this paper we consider linear systems given through a kernel representation P together with a quadratic cost functional H ̃ . We will see that the solvability of the associated infinite-horizon optimal control problem is equivalent to cyclo-dissipativity and that the solution of the optimal control problem can be obtained from the kernel representation of a para-Hermitian matrix polynomial which can be easily constructed from P and H ̃ . In contrast to previous work on this topic we avoid image representations as far as possible. sults can be applied to descriptor systems (see Section 4) to obtain results which so far were only known for regular descriptor systems with index 1 .