We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural con...

An canonical process is stationary independent increment uncertain process whose increments are normal uncertain variables. Uncertain differential equation is a type of differential equation driven by the canonical process. This paper will give a concept of stability in p-th moment for uncertain differential equations. A sufficient and necessary condition for linear uncertain differential equat...

Canonical process is a Lipschitz continuous uncertain process with stationary and independent increments, and uncertain differential equation is a type of differential equations driven by canonical process. This paper presents some methods to solve linear uncertain differential equations, and proves an existence and uniqueness theorem of solution for uncertain differential equation under Lipsch...

Multi-dimensional uncertain differential equation is a system of uncertain differential equations driven by amulti-dimensional Liu process. This paper first gives the analytic solutions of two special types of multi-dimensional uncertain differential equations. After that, it proves that the multi-dimensional uncertain differential equation has a unique solution provided that its coefficients s...

Uncertain differential equation with jumps, as a crucial tool to deal with a discontinuous uncertain system, is a type of differential equation driven by both canonical Liu process and uncertain renewal process. So far, a concept of stability in measure for an uncertain differential equation with jumps has been proposed. As a supplement, this paper proposes a concept of almost sure stability fo...

Abstract— This paper addresses robust consensus problems among multiple agents with uncertain parameters constrained in a given set. Specifically, the network coefficients are supposed polynomial functions of an uncertain vector constrained in a set described by polynomial inequalities. First, the paper provides a necessary and sufficient condition for robust firstorder consensus based on the e...

Uncertain differential equation is a type of differential equation driven by Liu process. So far, concepts of stability and stability in mean for uncertain differential equations have been proposed. This paper aims at providing a concept of almost sure stability for uncertain differential equation. A sufficient condition is given for an uncertain differential equation being almost surely stable...