Stability with initial data difference for nonlinear delay differential equations is introduced. This type of stability generalizes the known concept of stability in the literature. It gives us the opportunity to compare the behavior of two nonzero solutions when both initial values and initial intervals are different. Several sufficient conditions for stability and for asymptotic stability wit...

In this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H-norm for a singularly perturbed syste...

This paper addresses the stability of the switched systems with discrete and distributed time delays. By applying Lyapunov functional and function method, we show that, if the norm of system matrices Bi is small enough, the asymptotic stability is always achieved. Finally, a example is provided to verify technically feasibility and operability of the developed results. Keywords—Switched system,...

In this paper, the stability of switched linear systems is investigated using piecewise linear Lyapunov functions. Given a switched linear system, we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system. We assume that each individual subsystem is stable and admits a piecewise linear Lyapunov function. Based on these Lyapunov...

We introduce the concept of sos-convex Lyapunov functions for stability analysis of discrete time switched systems. These are polynomial Lyapunov functions that have an algebraic certificate of convexity, and can be efficiently found by semidefinite programming. We show that sos-convex Lyapunov functions are universal (i.e., necessary and sufficient) for stability analysis of switched linear sy...

A new stability theorem of the direct Lyapunov’s method is proposed for neutral-type systems. The main contribution of the proposed theorem is to remove the condition that the D operator is stable. In order to demonstrate the effectiveness, the proposed theorem is used to determine the stability of a neutral-type system in a critical case, i.e. the dominant eigenvalues of the principal neutral ...

Let S = {S 1, S 2} ⊂ Rd×d have a common, but not necessarily strict, Lyapunov matrix (i.e. there exists a symmetric positive-definite matrix P such that P − S T k PS k ≥ 0 for k = 1, 2). Based on a splitting theorem of the state space Rd (Dai, Huang and Xiao, arXiv:1107.0132v1[math.PR]), we establish several stability criteria for the discrete-time linear switched dynamics xn = S σn · · · S σ1 ...

New upper bounds for the solution of the discrete algebraic Lyapunov equation (DALE) P = APAT + Q are presented. The only restriction on their applicability is that A be stable; there are no restrictions on the singular values of A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability of A. The upper bounds are computable when the large dimension of A...

In this paper, new sufficient conditions for safe motion/force tracking control of robotic systems under unknown environment are proposed. The asymptotic stability conditions are proved using a Lyapunov impedance approach and the relationship between the error dynamics of the robotic system and its energy. A 3DOF manipulator constrained to a circular trajectory is finally used to validate the s...

Two efficient and numerically stable methods for the computation of the largest p Lyapunov characteristic exponents of an n dimensional discrete dynamical systems are presented.