A method based on conceptual tools of predictive control is described for solving set-point tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device, called command governor (CG), whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time a virtual sequence among a family of linearly parameterized command sequences, by solving a convex constrained quadratic optimization problem, and feeds the primal system according to a receding horizon control philosophy. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behavior, provided that an admissibility condition on the initial state is satisfied. Though the CG can be tailored for the application at hand by appropriately choosing the available design knobs, the required on-line computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem.Index Terms-Control under constraints, nonlinear feedback, predictive control, quadratic programming.

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This paper studies the frames corresponding to oversampled filter banks (FBs). For this class of FB frames, we present a state-space parameterization of perfect reconstruction FB frames and explicit and numerically efficient formulas to compute the tightest frame bounds, to obtain the dual FB frame, and to construct a tight (paraunitary) FB frame from a given untight (nonparaunitary) FB frame. The derivation uses well-developed techniques from modern control theory, which results in the unified formulas for generic infinite-impulse-response (IIR) and finite-impulse-response (FIR) FBs. These formulas involve only algebraic manipulations of real matrices and can be computed efficiently, reliably, and exactly without the approximation required in the existing methods for generic FBs. The results provide a unified framework for frame-theory-based analysis and systematic design of oversampled filter banks.