Westudy the stability of an analog optimization circuit that solves quadratic programming (QP) problems. The circuit dynamics are modeled as a switched affine system. A piece-wise quadratic Lyapunov function and the KYP lemma are used to derive the stability criterion. The stability criterion characterizes the range of critical circuit parameters for which the QP circuit is globally exponential...

Abstract In this paper, a stability control approach of flexible joint robot (FJR) based T-S fuzzy model using fuzzy Lyapunov function is proposed. First, the Takagi and Sugeno (T-S) fuzzy model is employed to approximate the flexible joint robot, then a fuzzy controller is developed based on parallel distributed compensation principle (PDC). The non-quadratic stability conditions for the flexi...

This paper considers an average consensus problem for multiple integrators over fixed, or switching, undirected and connected network topologies. Event based control is used on each agent to drive the state to their initial average eventually. An event triggering scheme is designed based on a quadratic Lyapunov function. The derivative of the Lyapunov function is made negative by an appropriate...

The problem of robust adaptive stabilization of a class of multi-input multi-output nonlinear systems with constant linearly parameterized uncertainty and unknown structure of bounded variation have been considered. With the aid of direct adaptive technique and control Lyapunov function method, a robust adaptive controller is designed to complete the globally adaptive stability of the closed-lo...

In this paper, we present a Lyapunov function for systems containing a double integrator and with controller saturation. This Lyapunov function is composed of a positive-semide"nite quadratic term and an integral term. The main result provides a su$cient condition that guarantees a system with a double integrator can be globally stabilized by a saturating linear controller. For a triple-integra...

−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...

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...

Stability problem for a class of linear continuous time and discrete time systems is well understood since long. This analysis has also been extended to switched linear systems with continuous and discrete descriptions. For such cases, arbitrary switching problem is addressed by constructing common quadratic and non-quadratic Lyapunov function. Moreover, keeping in view the invertible time dela...

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...