Purpose – The purpose of this paper is to present the methodology to the robust stability analysis of a vision-based control loop in an uncalibrated environment. The type of uncertainties considered is the parametric uncertainties. The approach adopted in this paper utilizes quadratic Lyapunov function to determine the composite Jacobian matrix and ensures the robust stability using linear matr...

A class of Lyapunov functions is proposed for discrete-time linear systems interconnected with a cone bounded nonlinearity. Using these functions, we propose sufficient conditions for the global stability analysis, in terms of linear matrix inequalities (LMI), only taking the bounded sector condition into account. Unlike frameworks based on the Lur’e-type function, the additional assumptions ab...

This paper introduces two different generalizations on non-quadratic stabilization of TakagiSugeno models via line-integral Lyapunov functions. Inspired in recent developments which have proved to relax the conservativeness in the quadratic framework via suitable matrix transformations, the results here provided outperform the existing ones for line-integral Lyapunov functions. Examples are pro...

This paper builds off of recent work on rapidly exponentially stabilizing control Lyapunov functions (RES-CLF) and control Lyapunov function based quadratic programs (CLFQP) for underactuated hybrid systems. The primary contribution of this paper is developing a robust control technique for underactuated hybrid systems with application to bipedal walking, that is able to track desired trajector...

In this paper we present various algorithms both for stability analysis and state-feedback design for discretetime piecewise aÆne systems. As in [9], our approach hinges on the use of piecewise quadratic Lyapunov functions that can be computed as the solution of a set of linear matrix inequalities. We show that the continuity of the Lyapunov function is not required in the discretetime case. Mo...

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 investigate the stability of hybrid systems in closed-loop with Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for both terminal cost and constraint set and terminal equality constraint hybrid MPC, even thou...

In this article, we study the finite-time stability (FTS) and finite time stabilization problems for a class of switched impulsive systems evolving on an arbitrary domain. This problem is formulated using scale theory where domain can be continuous, discrete, union disjoint intervals with variable gaps lengths or any combination these. Using common Lyapunov-quadratic Lyapunov-like functions, es...

We establish a nonlinear real estate model based on cobweb theory, where the demand function and supply function are quadratic. The stability conditions of the equilibrium are discussed. We demonstrate that as some parameters varied, the stability of Nash equilibrium is lost through period-doubling bifurcation. The chaotic features are justified numerically via computing maximal Lyapunov expone...

This paper deals with the problem of regional stability and performance analysis for a class of nonlinear discrete-time systems with uncertain parameters. We use polynomial Lyapunov functions to derive stability conditions and performance criteria in terms of linear matrix inequalities (LMIs). Although the use of polynomial Lyapunov functions is common for continuoustime systems as a way to red...