Simultaneous LQ optimal control design for discrete-time systems and sampled-data systems

This paper is concerned with simultaneous LQ optimal control design for discrete-time and sampled-data systems. First it is shown that discrete-time simultaneous LQ design problem of a set of discrete-time systems can be reduced to solving a set of coupled matrix inequalities. An iterative LMI algorithm is presented to solve the feasibility and the feedback gain. Then simultaneous stabilization and simultaneous LQ optimal control of a set of LTI continuous-time systems is considered via piecewise constant output feedback. It is shown that the design of a periodic piecewise constant feedback gain simultaneously minimizing a set of given continuous-time performance indexes for a set of LTI continuous-time systems can be reduced to that of a constant feedback gain minimizing a set of equivalent discrete-time performance indexes for a set of LTI discrete-time systems. Explicit algorithms for computing the equivalent discrete-time systems and performance indexes are derived. Examples are used to demonstrate the effectiveness of the proposed method.