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...

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...

esses etc, can be appropriately described by the switched model [3-8]. In this paper, we proposed an innovative representation modeling of the Takagi-Sugeno (T-S) fuzzy switched discrete-time system. The simulation of stability analysis methods based on Lyapunov stability theorem to study the stability and switching law design for the T-S fuzzy switched discrete-time systems. Sufficient conditi...

Abstract: The paper presents a method of determining the Lyapunov quadratic functional for linear time-invariant system with knon-commensurate neutral type time delays. The Lyapunov functional is constructed for its given time derivative, which is calculated on the trajectory of the system with k-non-commensurate neutral type time delays. The presented method gives analytical formulas for the c...

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...

A dynamic triopoly game characterized by firms with different expectations is modeled by threedimensional nonlinear difference equations, where the market has quadratic inverse demand function and the firm possesses cubic total cost function. The local stability of Nash equilibrium is studied. Numerical simulations are presented to show that the triopoly game model behaves chaotically with the ...