Note on the design of linear systems with piecewise constant feedback gains

The purpose of this correspondence is to report some relations that can be used to extend the scope of a computational algorithm for the suboptimal design of linear regulator systems. This algorithm was presented in [1], and can be used to determine suboptimal piecewise constant feedback gains to be used instead of the optimal continuously time-varying ones [3]. This correspondence deals with the extension to the case where, in addition to the piecewise constant gains, the switching times are also optimized.