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This article studies the energy-to-peak filter design problem for the continuous-time nonlinear singular system. A Takagi–Sugeno fuzzy model is constructed to represent the nonlinear plant. The article focuses on the fuzzy filter design for singular system, such that the formulated filtering error system is admissible (regular, impulse-free, and stable) and ensures the corresponding filtering performance in the singular system. By introducing a novel Lyapunov function, design conditions of the fuzzy filter for the continuous-time singular system are proposed in the light of linear matrix inequalities representations. Finally, a practical example and the relevant simulation results are provided to demonstrate the effectiveness and feasibility of the proposed energy-to-peak filter design approach. [ABSTRACT FROM AUTHOR]

This paper investigates a stabilization problem for linear systems subject to saturation and time-varying delays in the control input, where the delay takes both large and small values in an alternating manner. Based on the delay values, the considered system is described by a switched system including a stabilizable subsystem and an unstabilizable subsystem. By using Lyapunov–Krasovskii functional method, a time-dependent switching rule orchestrating the proposed controllers is established to guarantee the regional stabilization of the closed-loop system. To obtain a domain of attraction as large as possible, an optimization problem is formulated in the form of linear matrix inequalities. Numerical examples and simulations are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and ${l_{2}}$ -gain analysis are investigated for discrete-time switched systems with mode-dependent average dwell time (DT). By proposing a novel multiple discontinuous Lyapunov function (MDLF) approach, the conditions of stability and weighted ${l_{2}}$ -gain are established for nonlinear systems. Next, the corresponding results for linear switched systems are also proposed by using MDLF. It turns out that our proposed results provide smaller bounds on the DT. Some simulation results are given to show the validity of our approaches. [ABSTRACT FROM AUTHOR]

When designing interval observers for switched systems, for simplicity, it is always assumed that the switching signal of interval observers is synchronised with one of subsystems. However, in fact, they are asynchronous in most cases. In this study, the interval observer design problem for discrete‐time switched systems with asynchronous switching law is investigated. At first, a robust observer is designed based on the H∞ observer theory. Then, in order to reduce the conservatism of design conditions and improve the performance of the interval observer, the zonotope method is applied to estimate the bounds of system state. Finally, two examples are provided to highlight the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses stability and l2‐gain for discrete‐time switched systems with unstable modes based on slow/fast mode‐dependent average dwell time (MDADT) switching strategies. Firstly, by employing a class of multiple discontinuous Lyapunov functions (MDLFs) and developing a kind of alternative switching signals, the sufficient conditions on stability are established for the system without external disturbances under a slow/fast MDADT switching scheme with a tighter bounds on the dwell time. Furthermore, by defining indicator functions and exploring the features of slow/fast MDADT switching, the weighted l2‐gain conditions are achieved for the system with external disturbances. Particularly, the criteria of stability and l2‐gain are also established for the corresponding discrete‐time switched linear systems with unstable modes via the MDLFs method and the slow/fast MDADT switching strategy. Finally, two numerical examples are presented to illustrate the advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

In this study, the design problem of multiple‐mode observer and multiple‐mode controller is studied for switched positive linear systems. By proposing a new design approach for a class of switched positive linear system, numerical conditions for the existence of multiple‐mode observer and multiple‐mode controller are presented by using linear programming approach. First, a multiple‐mode observer is designed such that the error system is exponentially stable. Next, a robust multiple‐mode interval observer is presented for uncertain switched positive systems with uncertain parameters. In the sequel, a multiple‐mode output‐feedback controller is designed such that the closed‐loop system is exponentially stable. Compared with the existing references, the design method can bring out lower computational burden. Finally, three examples are given to show the effectiveness of the authors' results. [ABSTRACT FROM AUTHOR]

In this study, the authors analyse the stability of switched positive linear time‐delay systems. By developing a novel multiple discontinuous co‐positive Lyapunov–Krasovskii functional approach, the stability conditions are established for switched positive time delay systems by a linear programming approach under mode‐dependent average dwell time switching. Moreover, under average dwell time switching, the corresponding stability conditions are also proposed. It is shown that their results can obtain smaller lower bounds on dwell time. Finally, simulation results are given to show the effectiveness of their methods. [ABSTRACT FROM AUTHOR]

This correspondence paper is concerned with observer design problems for a class of unknown input switched descriptor systems under average dwell time switching signals. The switched descriptor system under consideration is first transformed into a general switched linear system, and then a switched reduced-order observer that can asymptotically estimate the system state without suffering the influence from the unknown inputs is developed. Besides, a high-order sliding mode observer is introduced to obtain the estimations of the output derivatives by using the system measured outputs. On the basis of estimations of the states and output derivatives, an unknown input reconstructing method is provided. Finally, two examples are presented to verify the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and stabilization for switched systems with mode-dependent average dwell time (MDADT) switching are revisited and discussed in both continuous-time and discrete-time contexts. By introducing a class of quasi-alternative switching signals, some improved stability conditions of switched systems with MDADT are obtained. In our switching design strategy, slow switching and fast switching are, respectively, used among stable subsystems and unstable subsystems. Then, based on the stability result, stabilization conditions for switched linear systems comprising uncontrollable subsystems are presented to guarantee the underlying system to be exponentially stable. The criteria obtained for the considered switched linear systems are all provided in terms of a set of linear matrix inequalities. To illustrate the advantages of our established results, a numerical example is finally given. [ABSTRACT FROM AUTHOR]

The problem of stability for discrete-time switched linear systems (DSLSs) with unstable subsystems is investigated. Unlike most existing results that require each switching mode of the system to be asymptotically stable, this paper considers the case that each subsystem may be unstable. First, under certain hypotheses, a necessary condition of stability for DSLSs is obtained. Second, using the average dwell time (ADT) strategy, some sufficient conditions of exponential stability for switched linear systems are derived under two assumptions. Finally, two examples are presented to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive control for a class of continuous-time switched linear systems is studied using a state-dependent switching method. All subsystems of the switched system under study can be unstable. First, an adaptive controller and a variable structure (VS) switching law with sliding sector are proposed, and some conditions are established in terms of linear matrix inequalities to guarantee the underlying system to be asymptotically stable. Then the problem of robust $$H_{\infty }$$ control for the systems under study is also solved by designing a proposed adaptive controller and a VS switching law. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problems of state estimation are investigated for switched linear systems with average dwell time (ADT) switching in both continuous-time and discrete-time contexts. First, a set of mode-dependent Luenberger-type observers is designed subject to the ADT switching that is synchronous with the switching of the estimated systems. Then, a more practical case of the delayed observers is also considered, which implies that the switching of the multiple-mode observer to be designed has a lag to the switching of the estimated systems. In this case, the asynchronous switching signals are combined as a preliminary attempt, upon which sufficient conditions for the existence of the Luenberger-type observers and the corresponding ADT switching are formulated in terms of a set of linear matrix inequalities. Finally, the proposed approaches are applied to the state estimation of electronic circuits to demonstrate the effectiveness and applicability. [ABSTRACT FROM PUBLISHER]

This article is concerned with the disturbance attenuation properties of a class of switched linear systems by using a mode-dependent average dwell time (MDADT) approach. The proposed switching law is less strict than the average dwell time (ADT) switching in that each mode in the underlying system has its own ADT. By using the MDADT approach, a sufficient condition is obtained to guarantee the exponential stability with a weightedH∞performance for the underlying systems. A numerical example is given to show the validity and potential of the developed results on improving the disturbance attenuation performance. [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]

Abstract: In this paper, the stability analysis problem for a class of switched positive linear systems (SPLSs) with average dwell time switching is investigated. A multiple linear copositive Lyapunov function (MLCLF) is first introduced, by which the sufficient stability criteria in terms of a set of linear matrix inequalities, are given for the underlying systems in both continuous-time and discrete-time contexts. The stability results for the SPLSs under arbitrary switching, which have been previously studied in the literature, can be easily obtained by reducing MLCLF to the common linear copositive Lyapunov function used for the system under arbitrary switching those systems. Finally, a numerical example is given to show the effectiveness and advantages of the proposed techniques. [Copyright &y& Elsevier]

This paper proposes improved delay-range-dependent H performance conditions and a H filtering algorithm for linear systems with interval time-varying delays. The proposed filtering approach guarantees that the results are less conservative than those obtained by other existing approaches. Numerical examples well demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

• Propose two prescribed time observers for LPV systems. • State estimation can be achieved in an arbitrarily prescribed time step. • The pole placement of observers only requires solving finite number of LMIs. This paper considers prescribed-time observer (PTO) designs for a class of linear parameter-varying (LPV) systems. Firstly, a full-order prescribed-time observer with time-varying gains is developed. The existence conditions are given in terms of linear matrix inequalities (LMIs). In addition, the reduced-order PTO is also considered in this paper. Moreover, it is shown that the existence conditions under which the full-order PTO exists can also guarantee the existence of a corresponding reduced-order PTO. The advantages of the full-order and the reduced-order PTOs over the existing asymptotic convergence observers are that (1) they can achieve exact estimations in almost any prescribed convergence time regardless of what the system initial values are. (2) the proposed time-varying gain PTOs can avoid the conservatism of the unknown input decoupling conditions brought about by the traditional polytopic LPV observer design methods. Finally, two examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

• This paper further investigates the design problem of the functional interval observer for discrete-time systems with disturbances and mainly has three highlights: • We design an FIO for linear discrete-time systems by using monotone system theory, and the sufficient conditions are presented by Sylvester equations. • The design constraints are reduced and the estimation accuracy is improved by using the zonotope method. • By comparing the two methods, the approach of the zonotope can reduce the constraints of observer design and improve the performance of the proposed FIO. This paper further investigates the design problem of the functional interval observer for discrete-time systems with disturbances. Two methods are given to design functional interval observers. Given monotone system theory, a Luenberger-like functional interval observer is constructed and sufficient conditions are achieved by Sylvester equations in the first method. The second approach is known as the two-step method. An H ∞ functional observer of the system is presented by the H ∞ technique, and then the approach of the zonotope is used to estimate its upper and lower boundaries to improve the estimation accuracy. The above methods are applied to two examples for comparison and to show the correctness. [ABSTRACT FROM AUTHOR]

• Optimal control problem of proportional delay systems is solved by an indirect method. • Initial guess on costate variables is avoided due to the benefit of successive convexification (SCvx) technique. • Each sub-problem is transformed into a system of linear algebraic equations with a sparse coefficient matrix. • Converged solutions can be obtained within a few iterations with an exponential convergent rate. • Both linear or exponential convergence property is exhibited by tuning the number of mesh and the LGL degree. In this paper, we propose an iterative framework to solve optimal control for nonlinear proportional state-delay systems. The successive convexification technique is first implemented to convert the original nonlinear problem into a sequence of linear-quadratic problems. And a symplectic pseudospectral method, where the multi-interval pseudospectral scheme is applied with a proportional mesh, to solve the transformed problems is then developed based on the first-order necessary conditions. Each linear-quadratic problem is finally transformed into a system of linear algebraic equations with a sparse coefficient matrix. Due to the benefit of the successive convexification technique and the multi-interval pseudospectral method, initial guess on costate variables is avoided and converged solutions can be obtained with an exponential convergent rate. The proposed iterative framework is validated by four examples with distinct features, highlighting its numerical precision and efficiency. And either exponential or linear convergence property can be exhibited by tuning the approximation degree or the mesh number. [ABSTRACT FROM AUTHOR]