We derive a new general jump condition on a broken Weierstrass-Erdmann extremal of a vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity, are ubiquitous in shape optimization and in the theory of elastic phase transformations. The new condition, which does not have a one dimensional analog, reflects the stationarity of the singular surface with respect t...

A sufficient condition for the open loop system to be regular, causal and stochastically stable is proposed for a class of discrete-time descriptor Markov jump systems with partly unknown transition probabilities. The proposed criteria are in the form of a set of strict linear matrix inequalities and convenient for numerical realization. The presented condition used the information of unknown t...

A free non-relativistic particle moving in two dimensions on a half-plane can be described by self-adjoint Hamiltonians characterized by boundary conditions imposed on the systems. The most general boundary condition is parameterized in terms of the elements of an infinite-dimensional matrix. We construct the Brownian functional integral for each of these self-adjoint Hamiltonians. Non-local bo...

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic quadratic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are...

This paper investigates the static output-feedback mixed H2/H∞ control problem of discrete-time Markovian jump systems from a novel perspective. Unlike traditional methods, the closed-loop system is represented as an augmented form, in which input and gain-output matrices are decoupled. By virtue of the augmented representation, new characterizations on stochastic stability and H2/H∞ performanc...

This paper is concerned with the problem of robust stability of Markovian jump singularly perturbed descriptor systems with uncertain switchings and nonlinear perturbations for any 2 .0, N , where N is a pre-defined positive scalar. A linear matrix inequality (LMI) condition is firstly established to guarantee the existence and uniqueness of a solution. Then, an -independent condition in terms ...