Overlapping quadratic optimal control of linear time-invariant systems and a commutative class of continuous-time time-varying systems has been recently developed by using a generalized structure of complementary matrices. It has been shown that these structures offer a powerful and effective mean for decentralized control design for these classes of systems. In this paper, these structures are...

In this paper we describe some initial ideas of a new lower bound technique which captures, in a strong way, the structure of optimal circuits. The key observation is that optimal circuits are unstable not only with respect to deletion of gates but also with respect to renaming gates. In some cases such an unstability allows one to extract some useful information about the inner structure of op...

A general approach is presented for the robust stabilization of controllable systems. The proposed strategy is viable whenever one can compute a finite-time control law that steers the state from any initial condition to a point closer to the desired equilibrium. Under suitable hypotheses, such control law can be applied in an iterative fashion, obtaining exponential convergence of the state to...

The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within its frame, the third evolution equation is developed. This equation only solves the control variables along the variation time to get the optimal solution, and...

For a broad class of nonlinear regression models we investigate the local Eand c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrema of the equi-oscillating best approximation of the function f0 ≡ 0 by a normalized linear combination of the regression functi...

A variant factor (VF) technique is developed for the control design of a class of single-input and single-output affine nonlinear systems with input saturation. The main ideas of VF are to convert an affine nonlinear system into a linear time-invariant system similar to the dynamic inversion and then to use the ideas of the composite nonlinear feedback (CNF) technique to design a control law fo...

Two seemingly independent streams of control systems research have examined logarithmic sensitivity integrals and limiting linear quadratic optimal control problems. These apparently diverse problems yield some results with an identical right hand side. The main contribution of this paper is to directly explain the commonality between these streams. This explanation involves the use of Parseval...