A novel approach to <i>L</i><sub>1</sub> filter design for asynchronously switched positive linear systems with dwell time

Li, Yang; Du, Wenju; Xu, Xiaozeng; Zhang, Hongbin; Xia, Jianwei

doi:10.1002/rnc.4702

Cited by 20 publications

(15 citation statements)

References 73 publications

(176 reference statements)

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“…Definition 1 (Average dwell time): For any switching rate σ(t), it is used to control switched system (1), denote N σ(t) (t 1 , t 2 ) as the switching times during the interval (t 1 , t 2 ). If there exists T a > 0, (16) satisfies, where χ(t) = e x T (t) e ξ T (t) T , then the system (14) and (15) is said to be exponentially stable.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

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Fault estimation for continuous‐time non‐linear switched systems with time‐varying delay based on intermediate estimator

Wang

Zhu

et al. 2020

IET Control Theory & Appl

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In this work, the fault estimation (FE) problem is studied for continuous-time non-linear switched systems with timevarying delay over fading channel under average dwell time switching. A novel FE method based on the intermediate estimator is used to eliminate the observer matching constraint condition, where an intermediate variable is introduced to estimate the state and fault simultaneously. Meanwhile, the fading channel of data transmission is modelled as Bernoulli distributed white sequences. Furthermore, because the observer matching conditions are eliminated by the intermediate estimator, both the wirtinger integral inequality and an advanced reciprocal convex combination method are utilised to provide a tighter estimation on continuous derivative of certain Lyapunov-Krasovskii function over fading channel, leading to a less conservative result. Moreover, the solution of the parameters for intermediate estimator is characterised in the feasibility of linear matrix inequality problem. Finally, two numerical examples indicate the proposed technique is valid and superior.

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Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…For example, the stability and stabilisation of switched systems are investigated in [1,[6][7][8][9][10][11]. The controller design of switched systems under asynchronous switching is studied in [12][13][14][15][16]. The H ∞ filtering for switched linear systems is discussed in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Fault estimation for continuous‐time non‐linear switched systems with time‐varying delay based on intermediate estimator

Wang

Zhu

et al. 2020

IET Control Theory & Appl

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“…Stability analysis is a basic problem for switched positive systems. In recent years, due to the wide application of switched positive systems in many fields, many stability and stabilization results related to switched positive systems have been obtained in References .…”

Section: Introductionmentioning

confidence: 99%

Reachable set estimation for switched nonlinear positive systems with impulse and time delay

Zhang

Sun

2020

Intl J Robust & Nonlinear

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This paper deals with the reachable set estimation for the continuous-time switched nonlinear positive systems with impulse, disturbance, and mixed time-varying delays under the average dwell time switching. Based on a method developed in positive systems, sufficient conditions are established such that all solutions of the system converge exponentially to a ball. Both the bound of the reachable set and the convergence rate are determined explicitly. Compared with the existing result, the average dwell time given in this paper is less conservative. Finally, numerical examples demonstrate the effectiveness of our results. K E Y W O R D S disturbance, impulse, reachable set estimation, switched positive system, time delay INTRODUCTIONNoting that absolute temperature, absolute potential, concentration of chemical reactants, and the number of biological insects are all taken nonnegative values, the corresponding dynamic systems can be described by positive systems. Positive systems are dynamic systems with positive constraints on state variables. 1 Switched positive system is composed of a series of positive subsystems and rules that determine the switching between subsystems. Stability analysis is a basic problem for switched positive systems. In recent years, due to the wide application of switched positive systems in many fields, many stability and stabilization results related to switched positive systems have been obtained in References 2-15. In many practical control systems, time delays are often encountered, such as environmental systems, chemical process systems, transmission systems, and so on. Time delay is often the source of the system instability and poor performance. [16][17][18][19] For the stability of positive systems with time delay, relevant studies show that the asymptotic stability is insensitive to constant and bounded time-varying delays. 20 Therefore, positive systems with time delay have attracted much attention in recent years.Impulsive phenomenon is prevailing in many fields which means a physical quantity suddenly changes in a short period of time and quickly returns to its initial state. Impulses which contribute to dynamics of systems have been applied to many practical problems such as satellite orbit transfer, electrical engineering, stability and synchronization of chaotic secure communication systems, and so on. In the past few years, the control and analysis of impulse systems have been one of the hot spots, and significant progress has been made in References 21-25.Reachable set is a set of all possible states of the system under specific constraints, which defines the range of system state in normal operation. Therefore, the estimation of the state reachable set boundary is of great significance for the analysis of system stability and the diagnosis of system faults. Reachable set estimation of continuous-time linear time-varying systems with bounded perturbations was studied in Reference 26. In Reference 27, the authors discussed reachable set estimation for continuous-time and ...

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“…The stochastic stability and

ℒ_{1}

‐gain analysis are studied for positive fuzzy semi‐Markov jump systems with time‐varying delay in Reference 29. In Reference 30, the

ℒ_{1}

filtering problem is investigated for switched positive systems by constructing a clock‐dependent Lyapunov function. How to solve the finite‐time boundedness control problem with

ℒ_{1}

‐gain performance for IPSs by the hybrid state feedback control is still a meaningful and challenging work, which motivates our study.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time control via hybrid state feedback for uncertain positive systems with impulses

Park

2020

Intl J Robust & Nonlinear

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In this study, the finite‐time ℒ1 control for uncertain positive systems with impulses using a hybrid state feedback control mechanism is investigated. The hybrid state feedback double control strategy is utilized, which includes impulsive state control scheme and continuous state feedback control scheme. A type of time‐varying Lyapunov copositive function is constructed. Considering different impulsive effects, the finite‐time boundedness criterion is obtained by applying the average impulsive interval approach. In addition, sufficient conditions are proposed for finite‐time ℒ1 characterization analysis and the hybrid state feedback controller design. All the criteria can be checked by the linear programming approach succinctly. The relationships among the upper bound of the finite‐time interval, the frequency and intensity of impulses, and the minimum allowable ℒ1‐gain level are revealed. Numerical examples are used to illustrate the usefulness of the theoretical results.

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A novel approach to L₁ filter design for asynchronously switched positive linear systems with dwell time

Cited by 20 publications

References 73 publications

Fault estimation for continuous‐time non‐linear switched systems with time‐varying delay based on intermediate estimator

Fault estimation for continuous‐time non‐linear switched systems with time‐varying delay based on intermediate estimator

Reachable set estimation for switched nonlinear positive systems with impulse and time delay

Finite‐time control via hybrid state feedback for uncertain positive systems with impulses

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A novel approach to L1 filter design for asynchronously switched positive linear systems with dwell time

Cited by 20 publications

References 73 publications

Fault estimation for continuous‐time non‐linear switched systems with time‐varying delay based on intermediate estimator

Fault estimation for continuous‐time non‐linear switched systems with time‐varying delay based on intermediate estimator

Reachable set estimation for switched nonlinear positive systems with impulse and time delay

Finite‐time control via hybrid state feedback for uncertain positive systems with impulses

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A novel approach to L₁ filter design for asynchronously switched positive linear systems with dwell time