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The disturbance attenuation problem is of concern in the design of the state feedback control law.

In this paper, the disturbance attenuation properties for a class of linear hybrid systems are investigated, and a hybrid optimal persistent disturbance attenuation control problem is studied.

Finally, the optimal persistent disturbance attenuation controller synthesis problem is studied.

Matrix equations of the type (1a - 1b) are encountered in the indefinite linear quadratic (LQ) control problem [1], and the disturbance attenuation problem, which is in deterministic case the H ∞ control theory, for linear stochastic systems with both state- and input-dependent white noise.

Note that either (C1) or (C2) is implemented depending on whether the problem is flux-sum attenuation or intensification respectively.

The robust molecular noise attenuation problem will be systematically discussed for gene networks with multiple process delays from the nonlinear H∞ stochastic signal-processing perspective.

Based on the obtained model, mode-dependent fault detection filters are used for residual generator, the addressed fault detection problem is converted into nonlinear H∞ attenuation problem.

This problem is often manifested as an attenuation of exposure response curves in occupational studies at high exposure levels (Stayner et al. 2003).

A convex optimization problem is formulated to design the desired filters with minimized H∞ noise attenuation level bound.

In the second stage an optimisation problem is solved to determine the free parameter such that the disturbance attenuation and the fault identification requirements are accomplished.

The discrete-time disturbance attenuation problem for a class of Hamiltonian systems is considered.