Further improvement in delay‐dependent finite‐time stability criteria for uncertain continuous‐time systems with time‐varying delays

Stojanović, Sreten B.

doi:10.1049/iet-cta.2015.0990

Cited by 16 publications

(22 citation statements)

References 29 publications

(54 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that in practice, uncertain time‐varying parameters often exist such as the time‐varying mass of electromagnetic levitation system 15 due to the movement of passengers, loading of luggage, etc. Assumption 2 means that unknown delay

τ (t)

is only required to be finite and its bound is not known unlike 2,5,6,24 . Moreover,

τ (t)

can be fast‐varying without any restriction on time‐varying rate of the delay such as

\dot{τ} (t) < 1

considered in 8,24,25 . Note that the predictor control methods of Reference 1,4,6 are not directly applicable to our considered system () because there is no information on the upper bound and time‐varying rate of the delay.…”

Section: Problem Statementmentioning

confidence: 99%

Adaptive control of feedforward nonlinear systems with uncertain time‐varying parameters and an unknown time‐varying delay in the input

Choi

2020

Adaptive Control & Signal

View full text Add to dashboard Cite

Summary In this paper, we consider a global regulation problem for a class of feedforward nonlinear systems. The key features of our considered system are identified by the presence of uncertain time‐varying parameters associated with main diagonal states and input and an unknown time‐varying delay in the input. Moreover, the growth rates of nonlinearity and the input‐delay are only known to be finite. To solve our considered problem, we give a process to obtain a compact set that contains the allowed time‐varying parameters. Then, we propose an adaptive controller which handles both unknown growth rate of nonlinearity and input‐delay for system regulation. We carry out the rigorous system analysis and show the effectiveness of our proposed control scheme via an application example.

show abstract

τ (t)

is only required to be finite and its bound is not known unlike 2,5,6,24 . Moreover,

τ (t)

can be fast‐varying without any restriction on time‐varying rate of the delay such as

\dot{τ} (t) < 1

Section: Problem Statementmentioning

confidence: 99%

Adaptive control of feedforward nonlinear systems with uncertain time‐varying parameters and an unknown time‐varying delay in the input

Choi

2020

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

“…It can be seen from According to Remark 8, the optimal bound with minimum value of c 2 relies on the parameter , we can find feasible solution when 1.1 ≤ ≤ 3.57. Solving the optimation problem (23), the minimum value of c 2 is 10, when = 1.3994. Figure 4 shows the optimal value with different value of .…”

Section: Discretizationmentioning

confidence: 99%

“…Recently, the concept of finite-time stability has been revisited in the light of linear matrix inequalities (LMIs) techniques and Lyapunov functional theory [20][21][22]. For instance, further improvement in delay-dependent finite-time stability criteria was investigated for uncertain continuous-time systems with time-varying delays in [23]. In regard to finite time stability for time-varying system, Amato has made great contributions, see, for example [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

Chen

Sun

2019

Asian Journal of Control

View full text Add to dashboard Cite

This paper investigates the problem of finite time stability of linear time‐varying system with delay. By constructing an augmented time‐varying Lyapunov functional and using the Wirtinger‐type inequality deductively, delay‐dependent finite time stability conditions are derived and presented in terms of differential linear matrix inequalities (DLMIs). Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) by discretizing the time interval into equally spaced time distances, and an algorithm is given to solve the RLMIs. Examples illustrate the feasibility and effectiveness of the proposed method.

show abstract

“…Some work [1]- [5] have shown that time delay is the factor causes the instability and poor performance in nonlinear systems. In the real world, there exists a particular type of practical systems called positive systems whose states variables are confined to be positive (at least nonnegative) for any nonnegative initial condition [6]- [9].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Positive Polynomial Fuzzy-Model-Based Control Systems With Time Delay Under Imperfect Premise Matching

Lam

Song

et al. 2018

IEEE Trans. Fuzzy Syst.

View full text Add to dashboard Cite

Abstract-This paper deals with the stability and positivity analysis of polynomial-fuzzy-model-based (PFMB) control systems with time delay, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop, under imperfect premise matching. To improve the design and realization flexibility, the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. A sum-of-squares (SOS)-based stability analysis approach using the Lyapunov stability theory is employed to investigate the positivity and stability of the PFMB control systems and synthesize the polynomial fuzzy controller. In order to relax the stability results, we propose two methods: 1) membership functions are considered as symbolic variables in the stability analysis, 2) the property of the membership functions and the boundary information of the membership functions are considered in the stability analysis. A simulation example is given to illustrate the effectiveness of the proposed approach.Index Terms-Polynomial fuzzy-model-based (PFMB) control systems, Time Delay, Stability analysis, Mismatched premise membership functions, Sum of squares (SOS).

show abstract

Further improvement in delay‐dependent finite‐time stability criteria for uncertain continuous‐time systems with time‐varying delays

Cited by 16 publications

References 29 publications

Adaptive control of feedforward nonlinear systems with uncertain time‐varying parameters and an unknown time‐varying delay in the input

Adaptive control of feedforward nonlinear systems with uncertain time‐varying parameters and an unknown time‐varying delay in the input

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

Stability Analysis of Positive Polynomial Fuzzy-Model-Based Control Systems With Time Delay Under Imperfect Premise Matching

Contact Info

Product

Resources

About