−Critical condition is derived for parameter−dependent quadratic Lyapunov function for a polytope of matrices. Condition gives some critical points for the plant, such that it becomes impossible to get parameters of Lyapunov function. In this paper first design is proposed of the memory less feedback controller for uncertain dynamic system with time varying delay. It is assumed that uncertainti...

A novel approach to solve a stabilization problem of an active suspension system using a quarter car model is presented. We apply a combination of our results for the framework of the approximate based direct discrete-time design and the Euler based discrete-time backstepping technique. This stabilization problem is very interesting since utilizing a simple quadratic Lyapunov function brings th...

This paper studies the global asymptotic stability of a class of fuzzy systems. It demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant (LTI) switching systems. A necessary condition and a sufficient condition for the stability of such systems are given, and it is shown that under the sufficient condition, a common Lyapunov function exists for the LTI ...

In this paper, we consider a competition model between n species in a chemostat including both monotone and non-monotone growth functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. We construct a Lyapunov function whic...

An algorithm for evaluating the cost performance of discontinuous autonomous discrete-time piecewise affine systems is presented. The algorithm performs reverse reachability analysis and constructs a piecewise quadratic trajectory cost function over the entire region of attraction of the origin while explicitly taking into account the exact spatial evolution of the trajectories and the exact sw...

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

This note presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented here can be extended to handle a deadzone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn–Tucker) conditions for optimality ...

SIRS models with delay times (discrete or distributed) are studied. By means of Lyapunov functionals, we establish the global stability conditions of the equilibrium states. We will make ingenious linear combination of common quadratic, composite quadratic and Volterra-type functionals, for obtain a suitable Lyapunov functionals.