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The study is concerned with the filtering problem of discrete time positive switched delay systems under an improved delay-dependent persistent dwell time (PDT) switching, which includes delay-independent PDT switching as a special case. Under delay-dependent PDT switching, a pair of state bounding positive filters is designed such that the output of positive switched delay systems can be estimated at all times, and the effect of delay on PDT switching and the l1 performance is also discussed. Finally, a numerical example is presented to demonstrate the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of weighted H∞ filtering for a class of switched linear systems with two additive time-varying delays, which represent a general class of switched time-delay systems with strong practical background. Combining average dwell time (ADT) technique with piecewise Lyapunov functionals, sufficient conditions are established to guarantee the exponential stability and weighted H∞ performance for the filtering error systems. The parameters of the designed switched filters are obtained by solving linear matrix inequalities (LMIs). A modification of Jensen integral inequality is exploited to derive results with less theoretical conservatism and computational complexity. Finally, two examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A distributed dynamic output feedback control is designed by Scardovi and Sepulchre for the synchronisation of a network of identical linear systems, known as agents in literature. The design is based on some mild conditions allowing switching topology. However, it assumes that there is no time delay in signal transfer between the neighbouring agents. In this study, the authors extend their work to include known time delay in communications. Furthermore, the authors' design has some special features: (i) the delay can be arbitrary and only need to be uniformly bounded by a constant; (ii) the conditions that time delay should be the same and sufficiently small in some literature are not required here; and (iii) no local buffer is required to store past data because of time-delay effect. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of positive observers for switched positive linear systems with time-varying delays. Attention is focused on designing the positive observers such that the error switched systems are exponentially stable. Based on the average dwell time approach, sufficient conditions, which ensure the estimated error exponentially converges to zero, are formulated in a set of linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper is focused on global exponential stability of certain switched systems with time-varying delays. By using an average dwell time (ADT) approach that is different from the method in [P.H.A. Ngoc, On exponential stability of nonlinear differential systems with time-varying delay, Applied Mathematics Letters 25 (2012) 1208–1213], we establish a new global exponential stability criterion for the switched linear time-delay system under the ADT switching. We also apply this method to a general switched nonlinear time-delay system. A numerical example is given to show the effectiveness of our results. [Copyright &y& Elsevier]

The switching signal design for exponential stability with H∞ performance of uncertain switched linear discrete-time systems with interval time-varying delay is considered. Systems with norm-bounded parameter uncertainties are considered. By taking a new Lyapunov-Krasovskii (LK) function, sufficient conditions for the existence of a class of stabilizing switching laws are derived in terms of linear matrix inequalities (LMIs) to guarantee the considered switched time-delay system to be exponentially stable. The resulting stability criteria are of fewer matrix variables and are less conservative than some existing ones. In addition, numerical examples are illustrated to show the main improvement. [ABSTRACT FROM AUTHOR]

Abstract: The stabilization problem for a class of switched linear systems with average dwell time (ADT) switching is reinvestigated in this paper. State-feedback controllers are designed, which takes the more practical case, asynchronous switching, into account, where the so-called “asynchronous switching” indicates that the switchings between the controllers and the system modes are in the presence of a time delay. By combining the asynchronous switching, an improved stabilization approach is given, and existence conditions of the controllers associated with the corresponding ADT switching are formulated in terms of a set of linear matrix inequalities. A numerical example is given to show the validity and potential of the obtained theoretical results. [Copyright &y& Elsevier]

This paper is focused on delay-independent stability analysis for a class of switched linear systems with time-varying delays that can be unbounded. When the switched system is not necessarily positive, we first establish a delay-independent stability criterion under arbitrary switching signal by using a new method that is different from the methods to positive systems in the literature. We also apply this method to a class of time-varying switched linear systems with mixed delays. [ABSTRACT FROM AUTHOR]

The problem of L 2-gain analysis and control synthesis is studied for a class of uncertain discrete-time switched linear systems with time delay and saturating actuators by using the multiple Lyapunov functions method. With the state feedback controllers adopted beforehand, an analysis condition on disturbance tolerance is derived under which the operating state trajectory with zero initial condition will remain inside a bounded set in its proximity. Then with this condition at hand, the largest disturbance tolerance level is determined via the solution of a constrained optimisation problem. Then, a sufficient condition for the restricted L 2-gain over the set of tolerable disturbances is derived. The smallest upper bound on the restricted L 2-gain is also obtained by solving a constrained optimisation problem. Furthermore, when controller gain matrices are design variables, these optimisation problems are adjusted for solving the control design task. An illustrative numerical example is given to demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Abstract: Finite-time boundedness and finite-time weighted L 2-gain for a class of switched delay systems with time-varying exogenous disturbances are studied. Based on the average dwell-time technique, sufficient conditions which guarantee the switched linear system with time-delay is finite-time bounded and has finite-time weighted L 2-gain are given. These conditions are delay-dependent and are given in terms of linear matrix inequalities. Detail proofs are given by using multiple Lyapunov-like functions. An example is employed to verify the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the problem of stabilization via state feedback and/or state-based switching for switched linear systems with mode-dependent time-varying delays. By using the multiple Lyapunov functional method, we establish sufficient conditions that guarantee the switched system is stabilizable via state feedback and/or switching under time-varying delays with appropriate upper bounds. The main results are presented in terms of linear matrix inequalities (LMIs) which generalize some known results and can be easily tested by using the Matlab’s LMI Tool-box. [Copyright &y& Elsevier]

We use a Lyapunov-Krasovskii functional approach to establish the exponential stability of linear systems with time-varying delay. Our delay-dependent condition allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. A simple procedure for constructing switching rule is also presented. [ABSTRACT FROM AUTHOR]

The issue of state convergence property for perturbed switched linear time-delay systems is explored. By introducing the variation-of-constants formula, the conditions for state convergence property of perturbed switched linear time-delay systems are established, and the difficulties caused by the interactions between the switchings and the time delay are alleviated. Based on the general result of perturbed switched linear time-delay systems, under two different switching schemes, new delay-dependent and -independent stability criteria for switched linear systems with time delay are derived. Two numerical examples along with the respective simulation results are given to demonstrate feasibility and validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: A stability analysis of linear systems with stochastically varying delay is performed. It is assumed that the delay function has the form of a sawtooth with switches occurring at the arrival times of a homogeneous Poisson process. Several notions of stochastic stability are considered and corresponding stability criteria are derived. For two examples the different criteria are compared and the effect on stability of various deterministic approximations is examined. [Copyright &y& Elsevier]

Abstract: Stability switching hypersurfaces (SSH) of a general class of linear time invariant (LTI) multiple time delay systems (MTDS) are extracted. The number of delays and system order in this problem are given but they are arbitrarily large. Hence, the extraction of SSH becomes non-trivial. A novel and efficient procedure reveals the 3D projections of -dimensional SSH, without the need for finding the SSH. In achieving this, computation times required remain in the same order of magnitude independently of and . Case studies demonstrate the effectiveness of the approach. [Copyright &y& Elsevier]

Abstract: This paper deals with on-line identification of continuous-time systems with structured entries. Such entries, which may consist of inputs, perturbations or piecewise polynomial (time varying) parameters, can be defined as signals that can be easily annihilated. The proposed cancellation method allows to obtain non asymptotic estimators for the unknown coefficients. Application to delayed and switching hybrid systems are proposed. Numerical simulations with noisy data but also experimental results on a delay process are provided. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of exponential stability and stabilization of switched linear time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also time-varying. By using an improved Lyapunov–Krasovskii functional, a switching rule for the exponential stability and stabilization is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the results. [Copyright &y& Elsevier]

The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the one-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays. [ABSTRACT FROM AUTHOR]