We calculate the Clarke and Michel-Penot subdifferentials of the function which maps a symmetric matrix to its mth largest eigenvalue. We show these two subdifferentials coincide, and are identical for all choices of index m corresponding to equal eigenvalues. Our approach is via the generalized directional derivatives of the eigenvalue function, thereby completing earlier studies on the classi...

We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitates the encapsulation of the exact geometrical description of the manifold in the analysis when this is represented by B–splines or NURBS. Our ...

In this paper we consider the robust partial quadratic eigenvalue assignment problem for second-order control systems by state feedback. To simultaneously reduce the feedback norms and the sensitivity of the close-loop eigenvalues, we formulate the problem as an unconstraint minimization problem for a new proposed cost function. An explicit analytic expression of the gradient of the cost functi...

This paper addresses the partial state consensus problem ofmulti-agent systemswith second-order agent dynamics and proposes an asynchronous distributed consensus protocol for the case with switching interaction topology, time-varying delays and intermittent information transmission. ‘‘Partial state consensus’’ means reaching an agreement asymptotically with each other on part, but not all, of e...

The generalized second-order partial derivatives of 1/r , where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a spheroidal-regularization expression is illustrated on an ...

A wavelength-selective 2-order 1-by-8-port optical multicast filter bank is demonstrated utilizing microring resonators, achieving ~2.6× faster roll-off than 1-order design while maintaining highly uniform responses among all eight drop ports. OCIS codes: (130.3120) Integrated optics devices; (230.5750) Resonators; (230.0250) Optoelectronics.