Establishing robust asymptotical stability of uncertain systems affected by time-varying uncertainty is a key problem. LMI sufficient conditions have been proposed in the literature for addressing this problem based on homogeneous polynomial Lyapunov functions. Unfortunately, till now it has been unclear whether these conditions are also necessary. This paper proposes a proof in order to show t...

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for class of systems with parametric uncertainties and external disturbances. The primary goals the proposed are to guarantee system stability performance in presence time-dependent To meet specified objectives, LMI form is calculated as hierarchical control structure. Using Lyapunov function...

In this paper, we present an automatable decompositional method for the computation of Lyapunov functions for hybrid systems with complex discrete state spaces. We use graph-based reasoning to decompose hybrid automata into subgraphs, for which we then solve semidefinite optimization problems to obtain local Lyapunov functions. These local computations are made in a way that ensures that the fa...

The robust stability analysis and robust controller design for linear systems subject to time-invariant uncertainties have attracted considerable attention in robust control theory. Undoubtedly, the Lyapunov theory is one of the main approaches to deal with this problem. Description of uncertain linear time-invariant systems using convex polytope-type uncertainty has found its natural framework...

In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for adopting non-smooth ISS Lyapunov functions is that “multiple Lyapunov functions” are commonly used in the stability theory for hybrid systems. We will show that the e...

Abstract: In this paper we address the problem of Unknown input Observer (UIO) for a class of nonlinear time delay systems. We propose an observer design method using a particular Lyapunov function that leads to solving a Linear Matrix Inequality (LMI) condition ensuring the H∞ convergence of the estimation error. Indeed, we use a Lyapunov function depending on the disturbances in order to avoi...

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 note deals with the problems of robust H∞ control for uncertain stochastic systems with a time-varying delay in the state. Based on the Lyapunov stability theory and the stochastic analysis tools, delay-dependent sufficient condition is established in terms of weak coupling linear matrix inequality (LMI) equations. The equations are derived by constructing a more efficient Lyapunov functio...

This paper presents LMI conditions for stability analysis and synthesis of robust and gainscheduled state feedback controllers for discrete-time linear parameter-varying (LPV) systems. It is assumed that the system matrices have a homogeneous polynomial dependence of arbitrary degree on the time-varying parameters. The parameters are assumed to vary inside a polytope and have known bounds on th...

This paper presents an H controller synthesis method for discrete time fuzzy dynamic systems based on a piecewise smooth Lyapunov function. The basic idea of the approach is to design a piecewise linear state feedback control law and use a piecewise smooth Lyapunov function to establish the global stability with H performance of the resulting closed loop fuzzy control systems. It is shown that ...