This paper presents a nonlinear projection neural network for solving interval quadratic programs subject to box-set constraints in engineering applications. Based on the Saddle point theorem, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the interval quadratic optimization problems. By employing Lyapunov function approach, the global...

A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio $mathcal R_0$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   $mathcal{R}_0$, this state can be either endemic ($mathcal{R}_0> 1$), or infection-free ($mathcal{R}_0leq 1$). The global asymptotic stability of ...

We construct a class of linear Lyapunov functions for Volterra quadratic stochastic operator. Using these functions we improve known results about ω-limit set of trajectories of the Volterra quadratic operators.

This paper presents a constructive method for showing exponential stability of autonomous nonlinear systems consisting of state-dependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or is the result of an exact or approximative description of an arbitrary nonlinear vector field. Stability is shown by joining multiple local Lyapunov functio...

In a companion paper ('Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory'), Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are develo...

We show that new universality of Lyapunov spectra {λi} exists in Hamiltonian systems with many degrees of freedom. The universality appears in systems which are neither nearly integrable nor fully chaotic, and it is different from the one which is obtained in fully chaotic systems on 1dimensional chains as follows. One is that the universality is found in a finite range of large i/N rather than...

Predictive control of nonlinear systems subject to output and input constraints is considered. A fuzzy model is used to predict the future behavior. Two new ideas are proposed here. First, an added constraint on the applied control action is used to ensure the decrease of a quadratic Lyapunov function, and so guarantee Lyapunov exponential stability of the closed-loop system. Second, the feasib...

The issue of constrained output feedback receding horizon control (RHC) for Takagi-Sugeno systems is studied in this paper. strategy developed through parameterizing the infinite moves as a non-parallel distributed compensation (non-PDC) law. parameter-dependent non-PDC controller optimized manner. extended non-quadratic Lyapunov function serves to guarantee robust stability augmented closed-lo...

In this paper we study the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties making use of piecewise linear (polyhedral) Lyapunov functions. A given class of Lyapunov functions is said to be “universal” for the uncertain system under consideration if the robust stability of the system is equivalent to the existence of a Lyapunov func...

This paper is concerned with the stability and stabilization problem of a Takagi-Sugeno fuzzy (TSF) system. Using non-quadratic function (well-known integral Lyapunov candidate (ILF)) some lemmas, new sufficient conditions are established as linear matrix inequalities (LMIs), which solved stochastic fractal search (SFS). The main advantage technique used its small conservatives. Motivated by me...