A new equation for the linear regulator problem

In this article, a new equation is derived for the optimal feedback gain matrix characterizing the solution of the standard linear regulator problem. It will be seen that, in contrast to the usual algebraic Riccati equation which requires the solution ofn(n + 1)/2 quadratically nonlinear algebraic equations, the new equation requires the solution of onlynm such equations, wherem is the number of system input terminals andn is the dimension of the state vector of the system. Utilizing the new equation, results are presented for the inverse problem of linear control theory.