This paper is devoted to stability analysis and synthesis of uncertain systems subject to input saturation. A new parameter-dependent Lyapunov function analyzing approach is proposed to reduce the conservatism in stability analysis for the polytopic systems subject to input saturation. Some new stability conditions and a gain-scheduling controller design method are then developed by the LMI opt...

For discrete-time Takagi–Sugeno (TS) fuzzy systems, we propose an state-feedback fuzzy controller associated with a fuzzy weighting-dependent Lyapunov function. The controller, which is designed via parameterized linear matrix inequalities (PLMIs), employs not only the current-time but also the one-step-past information on the time-varying fuzzy weighting functions. Appropriately selecting the ...

The problem of time optimal control design is considered for a chain of integrators. The suboptimal solution based on Implicit Lyapunov Function (ILF) method is presented in the form of continuous stabilizing feedback. The Semi-Definite Programming (SDP) problem with the constraints in the form of Linear Matrix Inequalities (LMI) is obtained for tuning the optimal parameters. The suboptimal sol...

This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm proposed class systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These expressed in form linear matrix inequalities (LMI) which could be solved using solvers LMI Toolbox MATLAB. Two numerical examples to illustrat...

A computational approach is presented in this paper to construct local Lyapunov functions for autonomous dynamical systems with multiple isolated locally asymptotically stable (such as point-like, periodic, or strange) attractors. We consider of nonlinear ODEs, where the right-hand-side dynamic equations given form rational (i.e., fraction polynomials). The function searched a parameterized qua...

This paper extends the idea of switching T-S fuzzy systems with linear consequent parts to nonlinear ones. Each nonlinear subsystem is exactly represented by a T-S fuzzy system with Lure’ type consequent parts, which allows to model and control wider classes of switching systems and also reduce the computation burden of control synthesis. With the use of a switching fuzzy Lyapunov function, the...

Sufficient linear matrix inequality LMI conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditio...

In this paper, we present conditions for the stabilization and regulation of the tracking error for an n-dimensional minimum-phase system preceded by a Prandtl-Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. The common Lyapunov function theorem is utilized together with a Linear Matrix Inequality (LMI) conditio...

This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constr...

In this paper, the linear matrix inequality (LMI) conditions for output feedback control problems are presented. The underlying theory is based upon the necessary and sufficient conditions for static output feedback quadratic stabilizability of continuous time-invariant polytopic systems. The proposed two computationally simple LMI-based algorithms (the V-K iterative and non-iterative one) are ...