Output Feedback Controller Design: Non–iterative Lmi Approach

The static output feedback problem is one of the most important open questions in control engineering, [13]. Several solutions to this problem are available. The necessary and sufficient conditions for static output feedback stabilizability of linear continuous or discrete-time systems are given in [6] and [10] with iterative procedure to output feedback controller design. An approach based on linearquadratic regulator theory applying Lyapunov results to output stabilization was presented in [7] for continuous-time systems leading to an iterative solution of three coupled matrix equations. Iterative LMI based output feedback controller design using structurally constrained state feedback approach was developed in [14]. Output feedback stabilization of discrete-time systems employing LQ regulator theory [9], [8], [5] can be found in [3]. Robust static output feedback controller design procedure have been proposed in large number of references. Basically, in most of them the linearization approach [4] is used to obtain a stabilization controller. In the above papers the existence of output feedback controller solution or convergence of the proposed algorithms are not discussed. In this paper a non-iterative (non-linearization) approach to design of output feedback controller employing LQ theory with guaranteed cost is proposed for some class of linear continuous and discrete-time systems. The proposed approach is based on the LMI novel necessary and sufficient stability conditions for linear systems.