This article is concerned with the observer-based output feedback stabilization problem for a class of nonlinear systems that satisfies the one-sided Lipschitz and the quadratically inner-bounded conditions. The system model under consideration encompasses the classical Lipschitz nonlinear system as a special case. For such a system, we design the output feedback controller via constructing a full-order Luenberger-type state observer. Sufficient conditions that guarantee the existence of observer-based output feedback are established in the form of linear matrix inequalities, which are readily solved by the available numerical software. Moreover, the proposed observer-based output feedback designs are applied to a flexible link manipulator system. Finally, simulation study on the manipulator system is given to demonstrate the effectiveness of the developed control design.
The outbreak of COVID-19 seriously challenges every government with regard to capacity and management of public health systems facing the catastrophic emergency. Culture and anti-epidemic policy do not necessarily conflict with each other. All countries and governments should be more tolerant to each other in seeking cultural and political consensus to overcome this historically tragic pandemic together.
A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. When the function is bounded from below, it has a very unique property that two or more local minimum solutions are separated by one local maximum solution, or one saddle point. Our intension in this paper is to categorize all possible configurations of the double well potential functions mathematically. In part Numerical examples are provided to illustrate the important features of the problem and the mapping in between.
Dedication: This paper is dedicated to Professor Jiye Han on the occasion of his 80th birthday.A quadratic optimization problem with one nonconvex quadratic constraint is studied using the canonical dual approach. Under the dual Slater's condition, we show that the canonical dual has a smooth concave objective function over a convex feasible domain, and this dual has a finite supremum unless the original quadratic optimization problem is infeasible. This supremum, when it exists, always equals to the minimum value of the primal problem. Moreover, a global minimizer of the primal problem can be provided by a dual-to-primal conversion plus a "boundarification" technique. Application to solving * Corresponding author 1540007-1 Asia Pac. J. Oper. Res. 2015.32. Downloaded from www.worldscientific.com by THE UNIVERSITY OF WESTERN ONTARIO on 04/13/15. For personal use only. W. Xing et al.a quadratic programming problem over a ball is included and an error bound estimation is provided.
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