In this paper, a new guidance law is designed to improve the performance of a homing missiles guidance system in terminal phase. For this purpose first of all, the two dimensions equations of motion are formulated, then the approximation dynamic of missile control loop is added to these equations which are nonlinear whit unmatched uncertainty. Then, a new adaptive back-stepping method is develo...

In this paper, improved conditions for the synthesis of static state-feedback controller are derived to stabilize networked control systems (NCSs) subject to actuator saturation. Both of the data packet latency and dropout which deteriorate the performance of the closed-loop system are considered in the NCS model via variable delays. Two different techniques are employed to incorporate actuator...

— A well known Moser stability theorem states that a generic elliptic fixed point of an area-preserving mapping is Lyapunov stable. We investigate the question of Lyapunov stability for 4-dimensional resonant totally elliptic fixed points of symplectic maps. We show that generically a convex, resonant, totally elliptic point of a symplectic map is Lyapunov unstable. The proof heavily relies on ...

In this paper we consider various regularity results for discrete quasiperiodic Schrr odinger equations ? n+1 ? n?1 + V (+ n!)n = En with analytic potential V. We prove that on intervals of positivity for the Lyapunov exponent the integrated density of states is HH older continuous in the energy provided ! has a typical continued fraction expansion. The proof is based on certain sharp large dev...

We study the relationship between the Lyapunov exponents of the geodesic flow of a closed negatively curved manifold and the geometry of the manifold. We show that if each periodic orbit of the geodesic flow has exactly one Lyapunov exponent on the unstable bundle then the manifold has constant negative curvature. We also show under a curvature pinching condition that equality of all Lyapunov e...

Abstract. For linear time-invariant (LTI) state space systems it is well-known that its asymptotic stability can be related to solution properties of the Lyapunov matrix equation according to so-called inertia theorems. The question now arises how analogous results can be obtained for LTI descriptor systems (singular systems, differential-algebraic equations). The stability behaviour of a LTI d...

Introduction 1 1. Lyapunov exponents of dynamical systems 3 2. Examples of systems with nonzero exponents 6 3. Lyapunov exponents associated with sequences of matrices 18 4. Cocycles and Lyapunov exponents 24 5. Regularity and Multiplicative Ergodic Theorem 31 6. Cocycles over smooth dynamical systems 46 7. Methods for estimating exponents 54 8. Local manifold theory 62 9. Global manifold theor...

The well known Brockett condition a topological obstruction to the existence of smooth stabilizing feedback laws has engendered a large body of work on discontinuous feedback stabilization. The purpose of this paper is to introduce a class of control-Lyapunov function from which it is possible to specify a (possibly discontinuous) stabilizing feedback law. For control-affine systems with unboun...

In this paper we propose a numerical method for computing all Lyapunov coefficients of a discrete time dynamical system by spatial integration. The method extends an approach of Aston and Dellnitz (1999) who use a box approximation of an underlying ergodic measure and compute the first Lyapunov exponent from a spatial average of the norms of the Jacobian for the iterated map. In the hybrid meth...

Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff’s matrix tree theorem...