scholarly journals Exponential Stabilization of Impulsive Switched Systems with Time Delays Using Guaranteed Cost Control

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xiang Xie ◽  
Honglei Xu ◽  
Rong Zhang
Keyword(s):  
Switched Systems ◽  
Time Delays ◽  
Cost Control ◽  
Sufficient Conditions ◽  
Guaranteed Cost Control ◽  
Functional Method ◽  
Guaranteed Cost ◽  
Exponentially Stable ◽  
Impulsive Switched Systems ◽  
Impulsive Switched System

This paper investigates the stabilization problem for impulsive switched systems with time delays. First, exponential stability criteria of the delayed impulsive switched systems are established by use of the Lyapunov-Krasovskii functional method. Based on these results, sufficient conditions for the existence of a guaranteed cost control are also given. Subject to these sufficient conditions, the closed-loop impulsive switched system under the guaranteed cost control law will be exponentially stable with a guaranteed cost value.

scholarly journals Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Yurong Liu ◽  
Hamid Reza Karimi ◽  
Xiaohui Liu
Keyword(s):  
Cost Function ◽  
Discrete Time ◽  
Time Delays ◽  
Cost Control ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
Guaranteed Cost Control ◽  
Optimization Approach ◽  
Mixed Time Delays ◽  
Guaranteed Cost

The guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays. The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound. The associated cost function is of a quadratic summation form over the infinite horizon. The nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov-Krasovskii functionals and developing some new analysis techniques, sufficient conditions for the existence of guaranteed cost controllers are derived with respect to the given cost function. Moreover, a convex optimization approach is applied to search for the optimal guaranteed cost controller by minimizing the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.

scholarly journals Nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems

2019 ◽  
Vol 17 (1) ◽  
pp. 716-727
Author(s):  
Leipo Liu ◽  
Hao Xing ◽  
Xiangyang Cao ◽  
Xiushan Cai ◽  
Zhumu Fu
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Actual State ◽  
Time Control ◽  
Guaranteed Cost ◽  
Impulsive Switched Systems ◽  
Positive Observer

Abstract This paper considers the nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems(DPISS). Firstly, the positive observer and nonfragile positive observer are designed to estimate the actual state of the underlying systems, respectively. Secondly, by using the average dwell time(ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost finite-time controller are designed and sufficient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost finite-time stability(GCFTS). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

scholarly journals Switching Fuzzy Guaranteed Cost Control for Nonlinear Networked Control Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Linqin Cai ◽  
Zhuo Yang ◽  
Jimin Yu ◽  
Zhenhua Zhang
Keyword(s):  
Control Systems ◽  
Cost Control ◽  
Controller Design ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Guaranteed Cost Control ◽  
Networked Control ◽  
Nonlinear Networked Control Systems ◽  
Guaranteed Cost

This paper deals with the problem of guaranteed cost control for a class of nonlinear networked control systems (NCSs) with time-varying delay. A guaranteed cost controller design method is proposed to achieve the desired control performance based on the switched T-S fuzzy model. The switching mechanism is introduced to handle the uncertainties of NCSs. Based on Lyapunov functional approach, some sufficient conditions for the existence of state feedback robust guaranteed cost controller are presented. Simulation results show that the proposed method is effective to guarantee system’s global asymptotic stability and quality of service (QoS).

Guaranteed Cost Control for Fuzzy Bilinear Systems with Uncertain Parameters

2012 ◽  
Vol 433-440 ◽  
pp. 1723-1729
Author(s):  
Ze Feng Gao ◽  
Jun Chen ◽  
Fei Liu
Keyword(s):  
Cost Control ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Guaranteed Cost Control ◽  
Bilinear Systems ◽  
Linear Matrix ◽  
Main Theme ◽  
Control Laws ◽  
Guaranteed Cost

The main theme of this paper is to present robust guaranteed cost control laws for a class of fuzzy bilinear systems (FBS) with parametric uncertainties. First, the piecewise Lyapunov function (PLF) method is utilized to design a fuzzy controller, which ensures the robust asymptotic stability of the closed-loop system, and then the robust guaranteed cost control law is also proposed. Second, based on the Schur complement and some variable transformations, some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities (LMIs). Finally, a numerical example is utilized to demonstrate the validity and effectiveness of the proposed control scheme.

scholarly journals Guaranteed Cost Control for Exponential Synchronization of Cellular Neural Networks with Mixed Time-Varying Delays via Hybrid Feedback Control

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
T. Botmart ◽  
W. Weera
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Cost Control ◽  
Sufficient Conditions ◽  
Guaranteed Cost Control ◽  
Cellular Neural Networks ◽  
Exponential Synchronization ◽  
Time Varying ◽  
Delay Function ◽  
Guaranteed Cost

The problem of guaranteed cost control for exponential synchronization of cellular neural networks with interval nondifferentiable and distributed time-varying delays via hybrid feedback control is considered. The interval time-varying delay function is not necessary to be differentiable. Based on the construction of improved Lyapunov-Krasovskii functionals is combined with Leibniz-Newton's formula and the technique of dealing with some integral terms. New delay-dependent sufficient conditions for the exponential synchronization of the error systems with memoryless hybrid feedback control are first established in terms of LMIs without introducing any free-weighting matrices. The optimal guaranteed cost control with linear error hybrid feedback is turned into the solvable problem of a set of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method.

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