Robust finite‐time boundedness of H∞ filtering for switched systems with time‐varying delay

For switched system, switching behavior always affects the finite‐time stability property, which was neglected by most previous research. This paper investigates the problem of robust finite‐time boundedness of H_∞ filtering for switched systems with time‐varying delay. Sufficient conditions that can ensure finite‐time bounded and H_∞ filtering finite‐time stability are derived. Based on the average dwell‐time approach, the closed‐loop system trajectory stays within a prescribed bound. At last, numerical examples are given to illustrate the efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

A partitioning approach for H∞ control of singular time‐delay systems

This paper presents a new approach for delay‐dependent H_∞ stability analysis and control synthesis for singular systems with delay. By constructing an augmented Lyapunov–Krasovskii functional with a triple‐integral term, and using the partitioning technique, a bounded real lemma is presented to ensure the singular state‐delay system to be regular, impulse free and stable with γ‐disturbance rejection. The proposed result leads to significant performance improvement in system analysis and synthesis. Based on the criterion obtained, a homotopy‐based iterative LMI algorithm is developed to design a static output feedback controller. The feasibility and the effectiveness of theoretical developments are illustrated through numerical examples.Copyright © 2012 John Wiley & Sons, Ltd.     

Improved stability and stabilization approach to linear interconnected time‐delay systems

In this paper, we investigate the problems of delay‐dependent analysis and state‐feedback synthesis for a class of linear continuous‐time interconnected systems with time‐varying delays. An augmented Lyapunov functional is properly constructed for the individual subsystems and an improved free‐weighting method is deployed to exhibit the delay‐dependent dynamics. Delay‐dependent stability analysis is then performed to develop linear matrix inequalities (LMIs)‐based conditions under which the family of linear delay subsystems is asymptotically stable with a γ‐level ??₂‐gain for the nominal model. Extension to systems with convex bounded parameter uncertainties in all system matrices is also provided. All the required numerical computations are performed on the subsystem level. By delay‐dependent stabilization, we design a family of local state‐feedback schemes to guarantee that the closed‐loop subsystem enjoys the delay‐dependent asymptotic stability with a prescribed γ‐level ??₂‐gain. The developed results are tested on a representative example to illustrate the theoretical developments. Copyright © 2009 John Wiley & Sons, Ltd.     

H∞ control for linear switched systems with time‐varying delay and dead‐zone inputs via an adaptive memory controller

This paper deals with the problem of robust H_∞ control for linear switched systems with time‐varying delay and dead‐zone inputs. First, a new state‐dependent switching law is proposed for the switched system with stable and unstable subsystems. Based on the proposed switching law and using the scaled small gain theorem, a more general stability criterion for the switched delay systems is established. Second, an adaptive memory controller is proposed for the switched system with dead‐zone inputs. With the help of a two‐term approximation of the time‐varying delay, the proposed memory controller only depends on the bounds of the time‐varying delay. Sufficient conditions on the existence of the desired controller are formulated in terms of linear matrix inequalities. Three examples are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust H∞ control of stochastic time‐delay jumping systems with nonlinear disturbances

This paper deals with the problems of robust stabilization and H_∞ control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm‐bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed‐loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H_∞ control problem is to guarantee a specified H_∞ performance index, while still achieving the mean‐square exponential stability requirement for the closed‐loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H_∞ control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI‐based design methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust exponential l2 − l ∞ control for discrete‐time switched system: A cone complement linearization method

The robust exponential l₂ ? l _∞ control problem is considered in this paper for discrete‐time switched systems with both time‐varying delay and norm‐bounded parameter uncertainties. An exponential l₂ ? l _∞ performance index is first introduced for the discrete‐time switched systems. The designed controller is a memory exponential l₂ ? l _∞ controller. By introducing an average dwell time approach and a Lyapunov–Krasovskii functional technique, some sufficient criteria guaranteeing exponential stability are presented, and the desired memory exponential l₂ ? l _∞ controller is established by resorting to a cone complement linearization method. Some results on exponential stability using memoryless exponential l₂ ? l _∞ controller and asymptotical stability with traditional l₂ ? l _∞ performance index are also established. Finally, a numerical example is provided to demonstrate that the proposed approach can lead to less conservatism compared with the developed result using memoryless exponential l₂ ? l _∞ controller and asymptotical stability analysis with traditional l₂ ? l _∞ performance index. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay‐dependent robust H ∞ control for uncertain singular time‐delay system with Markovian jumping parameters

The problem of robust H _∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H _∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Observer‐based H∞ control for uncertain singular time‐delay systems with actuator saturation

In this paper, the observer‐based H_∞ control problem for uncertain singular time‐delay systems with actuator saturation is concerned. First, a delay‐dependent linear matrix inequality (LMI) condition is obtained which, guarantees that the uncertain singular time‐delay systems with actuator saturation are regular, impulse free, and asymptotically stable with H_∞ performance condition. Then, with this condition, the estimation of stability region and the design method of observer‐based H_∞ controller are given by solving LMIs and convex optimization problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.     

Delay‐dependent feedforward control of time‐delay systems with parametric uncertainties via dynamic IQCs

This paper studies the design problem of a robust delay‐dependent H _∞ feedforward controller design for a class of linear uncertain time‐delay system having state and control delays when the system is subject to ‐type disturbances. The proposed controller scheme involves two main controllers, which are static state‐feedback and dynamic feedforward controllers. The state‐feedback controller is used for stabilizing the delay and uncertainty‐free system, whereas the feedforward controller performs disturbance attenuation. Dynamic type integral quadratic constraints (IQCs), which consist of frequency‐dependent multipliers, have been introduced to represent the delays and parametric uncertainties in the system where the degree of the multiplier used in IQC representation is in an adjustable nature. This scheme allows the designer to obtain less conservative controllers with increasing precision. Sufficient delay‐dependent criteria in terms of linear matrix inequalities are obtained such that the uncertain linear time‐delay system is guaranteed to be globally, uniformly, asymptotically stable with a minimum disturbance attenuation level. Several numerical examples together with the simulation studies provided at the end illustrate the usefulness of the proposed design. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust H∞ control of linear time‐varying systems with mixed delays in the Hilbert space

In this paper, a class of linear infinite‐dimensional systems with discrete and distributed time‐varying delays is studied. New sufficient conditions for the robust H_∞ control of linear time‐varying control systems with mixed time‐varying delays in Hilbert spaces have been established. The conditions are given in terms of the solution of a Riccati differential equation. Furthermore, it is proved for the first time that the solution to the robust H_∞ control problem can be solved by the global controllability of an appropriate linear control delay‐like system. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved delay‐partitioning approach to robust stability analysis for discrete‐time systems with time‐varying delays and randomly occurring parameter uncertainties

This paper is concerned with the robust stability problem for uncertain discrete‐time systems with interval time‐varying delays and randomly occurring parameter uncertainties. By construction of a suitable Lyapunov–Krasovskii functional and utilization of new zero equalities with delay‐partitioning approach, improved delay‐dependent criteria for the robust stability of the systems are derived in terms of linear matrix inequalities for guaranteeing the asymptotic stability of the concerned systems. The effectiveness and reduction of conservatism of the derived results are demonstrated by three numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust ℋ︁2 static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems

This paper investigates the problem of computing robust ??₂ static output feedback controllers for discrete‐time uncertain linear systems with time‐invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter‐dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ??₂ guaranteed cost. The conditions are based on parameter‐dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H_∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.     

Time‐delay dependent H∞ model simplification for singular systems with Markovian jumping parameters

The problem of H_∞ model simplification for singular systems with Markovian jumping parameters and time‐delay is investigated. For a given stochastic stable system, our attention is focused on the construction of reduced‐order models which guarantee the corresponding error system to be admissible and have a prescribed H_∞ error performance. A robust admissibility condition and a robust bounded real lemma are developed based on which, sufficient conditions for the existence of desired reduced‐order models are proposed. Desired reduced‐order model can be constructed when the proposed conditions are satisfied. The effectiveness of the proposed model reduction method is illustrated via a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Delay‐dependent output feedback L1 control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates

The paper deals with the problem of delay‐dependent output feedback L₁ control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates. First, by constructing an appropriate co‐positive type Lyapunov function, sufficient conditions for stochastic stability and L₁‐gain performance of the open‐loop system are developed. Then, an effective method is proposed to construct the output feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, a numerical example is given to illustrate the validity of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ control for sampled‐data linear systems with two Markov processes

This paper is concerned with the design problem of H_∞ digital switching control for linear continuous systems with Markovian jumping parameters. The controller is digital and monitored by the jumping parameters of the plant. The closed‐loop system is a hybrid one defined on a hybrid time space (composed of a continuous‐time and a discrete‐time) and a sample space. The sample space is specified by two separable continuous‐time discrete‐state Markov processes, one appearing in the open‐loop system, and the other appearing in control action, which is different with the traditional Markovian jumping process. Our attention is focused on designing digital output feedback controllers for the system with two Markovian jumping processes such that both stochastic stability and a prescribed H_∞ performance are achieved. The problem of robust H_∞ control for systems with parameters uncertainties is also studied. It is shown that the sampled‐data control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled matrix inequalities. Two numerical examples are given to show the design procedures. Copyright © 2005 John Wiley & Sons, Ltd.     

Rejection of persistent‐bounded disturbances in linear time‐delay systems by output‐feedback

In this paper, the problem of persistent‐bounded disturbance rejection of linear continuous‐time systems with time‐varying delays is investigated using the tools of invariant set analysis and Lyapunov‐function methodology. We derive less conservative sufficient conditions on robust attractor for time‐delay systems in terms of strict linear matrix inequalities (LMIs) to guarantee the desired ??₁‐performance. A robust output‐feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on two representative time‐delay examples. Copyright © 2009 John Wiley & Sons, Ltd.