This article deals with some complementarity properties of Z and Lyapunov-like transformations on a symmetric cone. Similar to the results proved for Lyapunov and Stein transformations on Herm(Rn×n), we show that for Lyapunov-like transformations, the P and S properties are equivalent, and that for a Ztransformation, the S-property implies the P-property of a transformation that is (quadratical...

This paper deals with stability analysis of hybrid systems. Such systems are characterized by a combination of continuous dynamics and logic based switching between discrete modes. Lyapunov theory is a well known methodology for the stability analysis of linear and nonlinear systems in control system literature. Construction of Lyapunov functions for hybrid systems is generally a difficult task...

The construction of an input-to-state stability (ISS) Lyapunov function for networks of ISS system will be presented. First we construct ISS Lyapunov functions for each strongly connected component, then what remains is a cascade (or disconnected aggregation) of these strongly connected components. Using known results the constructed Lyapunov functions can be aggregated to one single ISS Lyapun...

In this paper we present suucient conditions for the controllability of the reduced dynamics of a class of mechanical systems with symmetry. We prove conditions (boundedness of coadjoint orbits and existence of a radially unbounded Lyapunov function) under which the drift vector eld (of the reduced system) is weakly positively Poisson stable (WPPS). The WPPS nature of the drift vector eld along...

In this paper, least squares support vector machine (LS-SVM) based motion control of a mobile robot in dynamic environment is proposed under the measured data with uncertainties. The proposed scheme can control the robot by consideration of local minima, where the controller is based on Lyapunov function candidate and considers virtual forces information. Comparing with standard support vector ...

support vector regression (svr) solves regression problems based on the concept of support vector machine (svm). in this paper, a new model of svr with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...

The Lyapunov theory of dynamical systems is the most useful general theory for studying the stability of nonlinear systems. It includes two methods, Lyapunov's indirect method and Lyapunov's direct method. Lyapunov's indirect method states that the dynamical system ˙ x = f (x), (1) where f (0) = 0, has a locally exponentially stable equilibrium point at the origin, if and only if the real parts...

This paper shows that Lyapunov-based state feedback controller synthesis for piecewise-affine (PWA) slab systems can be cast as an optimization problem subject to a set of linear matrix inequalities (LMIs) analytically parameterized by a vector. Furthermore, it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem withou...

in this paper, stabilization conditions and controller design for a class of nonlinear systems are proposed. the proposed method is based on the nonlinear feedback, quadratic lyapunov function and heuristic slack matrices definition. these slack matrices in null products are derived using the properties of the system dynamics. based on the lyapunov stability theorem and sum of squares (sos) dec...

We study Livsic's problem of nding satisfying X = where is a given function and X is a given Anosov vector eld. We show that, if is a continuous solution and X; are analytic, then is analytic. We use the previous result to show that if two low-dimensional Anosov systems are topologically conjugate and the Lyapunov exponents at corresponding periodic points agree, the conjugacy is analytic. Anal...