Initial and transient response improvement for singular systems

This paper deals with a generalized LQ regulator problem for singular systems with random initial states by output feedback. The idea of the generalization is to take care of instantaneous jumps, which generically exist at the initial time due to inconsistent initial states and can be arbitrarily large though they are finite in the absence of impulses. The problem is solved using the gradient flow approach. The designed output feedback will ensure that the closed-loop system has not only a satisfactory transient response but also significantly low instantaneous jumps with respect to any random initial state with given expectation and covariance.