Optimal noise rejection in structural analysis by means of generalized sampled-data hold functions (Q5928199)

The authors study controllable and observable linear state space systems of the form \[ \dot x(t)= Ax(t)+ Bu(t)+ w(t),\quad y(t)= Cx(t),\quad \xi(kT_0)= y(kT_0)+ v(kT_0), \] where \[ x(t)\in \mathbb{R}^n,\quad u(t)\in \mathbb{R}^m,\quad y(t)\in \mathbb{R}^p\quad\text{and}\quad w(t)\in \mathbb{R}^n \] are the state, control, output and disturbance vectors, respectively, \(T_0\) is the sampling period, and \(v(xT_0)\) is a discrete measurement noise vector. Using the results of \textit{P. T. Kabamba} from ``Control of linear systems using generalized sampled-data hold functions'' [IEEE Trans. Autom. Control AC-32, 772-783 (1987; Zbl 0627.93049)], the authors treat the optimal noise rejection problem in a structural control problem. The goal of their design objective here is to attenuate the detrimental effect of the disturbances (i.e. earthquake, impact of a ship vessel to a bridge pier etc.) on the system states to an acceptable level by minimizing a certain quadratic cost function. This minimization is performed by feeding back the outputs of the system, which are assumed to be corrupted by measurement noise. On the other hand, for such a type of optimal regulators, the robustness properties of the GSHF based optimal regulator is analyzed and expressed in terms of an elementary cost and system matrices. The theoretical results are illustrated by various simulation results.