We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of the stationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that de...

For both discrete-time and continuous-time linear multi-variable control systems, we introduce a concept of control Lyapunov modes associated with a control Lyapunov function in a quadratic form. We prove that the number of unstable control Lyapunov modes is at most equal to the number of input of the system.

A linear-quadratic control problem for some infinite-dimensional controlled stochastic differential equations driven by a fractional Gaussian noise is solved. The feedback form of the optimal control and the optimal cost are given. The optimal control is the sum of the well known linear feedback control for the associated deterministic linear-quadratic control problem and a suitable prediction ...

The discrete-time linear quadratic optimal problem with finite final time for a servo-drive system with a brushless or a dc motor is presented. The proposed algorithm allows simplifying the optimal control law implementation. The optimal control ensures a good behavior of the system and the decrease of the energy consumption. Key-Words:Optimal control, Brushless, DC machines, Efficiency, Servo ...

This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time-invariant model. An efficient algorithm for solving the Riccati equation is derived by...