This paper considers the robust stability problem for state space models via homogeneous polynomially parameter-dependent Lyapunov functions. The suggested approach is based on a quadratic in the vector of parametric monomials matrix representation of the time derivative of the Lyapunov function. At each step, sufficiency is provided by a set of relaxed linear matrix inequalities and check for ...

In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman’s equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target fun...

this paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy proportional-integrator-derivative (pid) controller with h∞ tracking performance. the purpose of this work is to achieve optimal tracking performance of the controller using backtracking search algorithm (bsa). bsa, which is a novel heuristic algorithm, has an easy structure with singl...

We consider the time-dependent nonlinear system q̇(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uni...

For many years now, the variety of problems of the qualitative properties of differential equations in the context of Lyaponov second method has been successfully investigated in a unified way using the comparison principle [S]. In this method, the qualitative properties of the system of differential equations are inferred from the corresponding properties of the solutions of the system of comp...

We present an approach for the stability-preserving model order reduction of switched linear systems with individual subspaces for arbitrary switching signals. First the high-order subsystems of the switched system are reduced by any reduction method and stabilized if necessary. Then the reduced subsystems are made contractive by solving low-dimensional Lyapunov equations. During time simulatio...

We present a new comparison principle by introducing a notion of upper quasi-monotone nondecreasing and obtain the practical stability criteria for set valued differential equations in terms of two measures on time scales by using the vector Lyapunov function together with the new comparison principle.

The data-driven approximation of vector fields that encode dynamical systems is a persistently hard task in machine learning. If data is sparse and given in form of velocities derived from few trajectories only, state-space regions exists, where no information on the vector field and its induced dynamics is available. Generalization towards such regions is meaningful only if strong biases are i...