The goal of this article is to provide a construction of a homogeneous Lyapunov function P associated with a system of differential equations J = f(x), x ~ R ~ (n > 1), under the hypotheses: (1) f ~ C(R n, ~ ) vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable. Moreover, the Lyapunov function V(x) tends to infinity with 1[ x [I, and belon...

Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multiobjective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lypaunov f...

We present constructions of a local and global common Lyapunov function for a finite family of pairwise commuting globally asymptotically stable nonlinear systems. The constructions are based on an iterative procedure, which at each step invokes a converse Lyapunov theorem for one of the individual systems. Our results extend a previously available one which relies on exponential stability of t...

The generalized methodology for the electronic networks optimization was elaborated by means of the optimal control theory approach. In this case the problem of the electronic system design is formulated as a classical problem of functional minimization of the optimal control theory. The minimal time system design algorithm was defined as a controllable dynamic process with an optimal control v...

This paper presents Lyapunov-based pursuit guidance law against stationary targets. To design a nonlinear guidance law, Lyapunov candidate function is introduced to reduce the angle between the velocity vector of a missile and the distance vector between the missile and the target. Therefore, the proposed guidance laws have the characteristic of pursuit guidance. To attack a target from a prede...

The generalized methodology for the electronic networks optimization system was elaborated by means of the optimal control theory approach. The problem of the electronic system design is formulated in this case as a classical problem of functional minimization of the optimal control theory. The minimal time system design algorithm was defined as a controllable dynamic process with an optimal co...

| In this note a continuous feedback control law with time-periodic terms is derived for the control of non-holonomic systems in power form. The control law is derived by Lyapunov design from a homogeneous Lyapunov function. Global asymptotic stability is shown by applying the principle of invariance for time-periodic systems. Exponential convergence follows since the vector elds are homogeneou...

in this paper, global uniform exponential stability of perturbed dynamical systemsis studied by using lyapunov techniques. the system presents a perturbation term which isbounded by an integrable function with the assumption that the nominal system is globallyuniformly exponentially stable. some examples in dimensional two are given to illustrate theapplicability of the main results.

a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

A linear complementarity system (LCS) is a piecewise linear dynamical system consisting of a linear time-invariant ordinary differential equation (ODE) parameterized by an algebraic variable that is required to be a solution to a finite-dimensional linear complementarity problem (LCP), whose constant vector is a linear function of the differential variable. Continuing the authors’ recent invest...