Robust D-stability analysis for linear discrete singular time-delay systems with structured and unstructured parameter uncertainties

In this paper, the robust D-stability problem (i.e. the robusteigenvalue-clustering in a specified circular region problem)of linear discrete singular time-delay systems with structured(elemental) and unstructured (norm-bounded) parameter uncertaintiesis investigated. Under the assumptions that the linear nominaldiscrete singular time-delay system is regular and impulse-free,and has all its finite eigenvalues lying inside a specifiedcircular region, a new sufficient condition is proposed to preservethe assumed properties when structured and unstructured parameteruncertainties are added into the linear nominal discrete singulartime-delay system. When all the finite eigenvalues are justrequired to locate inside the unit circle of the z-plane, theproposed criterion will become the stability robustness criterion.For the case that the linear discrete singular time-delay systemis only subject to structured parameter uncertainties, by anillustrative example, the presented sufficient condition isshown to be less conservative than the existing one reportedrecently in the literature.     

Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems: a comparison

We address the output feedback stabilization problem of linearfinite-dimensional SISO systems. Limitations of static time-invariantoutput feedback on stabilizability are well known. We investigateand compare the possibilities of two recently proposed simplemodifications/generalizations of static time-invariant outputfeedback to remove such limitations. The first approach consistsof introducing a time-delay in the control law, which can betreated as an additional control parameter. The second approachconsists of making the gain time-varying. We show that bothapproaches are complementary. Existing theoretical results arebrought together in a unifying framework. Numerical proceduresfor the construction of the controllers are provided. Robustnessw.r.t. both parametric and delay uncertainty are dealt with.As an illustration the stabilizability of all second-order systemsis completely determined.     

Robust stabilization of uncertain linear dynamical systems with time-varying delay

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh ^–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.     

Robust static output feedback variable structure control for nonlinear systems

In this paper, a robust stabilization problem for nonlinearsystems is investigated using static output feedback. Matchedand mismatched uncertainties are considered and their boundingfunctions take general forms. Based on a Lyapunov analysis approachand sliding mode techniques, some conclusions are presented.Then, a robust nonlinear variable structure control scheme issynthesized to stabilize the system globally, and it is notnecessary for the nominal system to be linearizable globally.The conservatism is reduced by using uncertainty bounds in thecontrol design. Finally, a mass–spring system is employedto illustrate the effectiveness of the results.     

Output feedback stabilization for planar switched nonlinear systems with asymmetric output constraints

In this paper, smooth output feedback controllers are presented to stabilize a class of planar switched nonlinear systems with asymmetric output constraints (AOCs). A new common barrier Lyapunov function (CBLF) is developed to prevent the switched system from violating AOCs. Combining the adding a power integrator technique (APIT) and the CBLF, state feedback controllers are designed. Then, reduced-order nonlinear observers are constructed and smooth output feedback controllers are proposed to globally stabilize planar switched nonlinear systems under arbitrary switchings. Meanwhile, the system output meets the prescribed AOCs during operation. The method proposed in this paper is a unified tool because it works not only for switched nonlinear systems with asymmetric or symmetric output constrains but also for those without output constraints. Simulations are presented to verify the proposed method.     

LMI‐based criterion for the robust guaranteed cost control of uncertain switched neutral systems with time‐varying mixed delays and nonlinear perturbations by dynamic output feedback

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time‐varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay‐dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water‐quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555–578, 2016     

Relaxed fuzzy observer‐based output feedback control synthesis of discrete‐time nonlinear control systems

This work develops the development of observer‐based output feedback control design of discrete‐time nonlinear systems in the form of Takagi–Sugeno fuzzy model. Lately, previous results have been improved in virtue of a two‐step method. From a technical point of view, it is not flawless and related problems have not been completely resolved. In this study, more advanced two‐steps approach is further developed while the relative sizes among different normalized fuzzy weighting functions are utilized by introducing some additional matrix variables. As a result of the above work, those main defects of the existing method can be redressed and a desired solution in aspect of not only reducing the conservatism but also alleviating the computation complexity is provided for some special cases. Moreover, the effectiveness of the proposed result is shown at length by means of an illustrative example. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–601, 2016     

State feedback and output feedback control of a class of nonlinear systems with delayed measurements

This paper is concerned with the problem of state feedback and output feedback control of a class of nonlinear systems with delayed measurements. This class of nonlinear systems is made up of continuous-time linear systems with nonlinear perturbations. The nonlinearity is assumed to satisfy a global Lipschitz condition and the time delay is assumed to be time-varying and have no restriction on its derivative. On the basis of the Lyapunov–Krasovskii approach, sufficient conditions for the existence of the state feedback controller and the output feedback controller are derived in terms of linear matrix inequalities. Methods of calculating the controller gain matrices are also presented. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Quadratic stabilizability of uncertain linear systems containing both constant and time-varying uncertain parameters

This paper is concerned with the problem of stabilizing an uncertain linear system using state feedback control. The uncertain systems under consideration are described by state equations containing unknown but bounded uncertain parameters. The uncertain parameters are classified into two types: either constant or time-varying. Indeed, the main feature of this paper is that it allows one to exploit the fact that some of the uncertain parameters are constant. In order to investigate the question of stabilizability, quadratic Lyapunov functions are used. Hence, the paper deals with the notion of quadratic stabilizability. The main result of the paper is a necessary and sufficient condition for the quadratic stabilizability of the uncertain systems under consideration.     

Consensus of heterogeneous multi-agent systems with linear and nonlinear dynamics

In this paper, we perform an in-depth study about the consensus problem of heterogeneous multi-agent systems with linear and nonlinear dynamics.Specifically, this system is composed of two classes of agents respectively described by linear and nonlinear dynamics. By the aid of the adaptive method and Lyapunov stability theory, the mean consensus problem is realized in the framework of first-order case and second-order case under undirected and connected networks.Still, an meaningful example is provided to verify the effectiveness of the gained theoretical results. Our study is expected to establish a more realistic model and provide a better understanding of consensus problem in the multi-agent system.     

Output feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays

This paper deals with output feedback guaranteed cost control problem for a general class of uncertain linear discrete delay systems, where the state and the observation output are subjected to interval time-varying delay. The proposed output feedback controller uses the observation measurement to exponentially stabilize the closed-loop system and guarantee an adequate level of system performance. By constructing a set of augmented Lyapunov–Krasovskii functionals, a delay-dependent condition for the robust output feedback guaranteed cost control is established in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the efficiency of the proposed method.     

New results on quadratic stabilization of switched linear systems with polytopic uncertainties

^** Corresponding author. Email: longwang{at}pku.edu.cn^*** Email: jizj{at}mech.pku.edu.cn In this paper, the quadratic stabilization of switched linearsystems with polytopic uncertainties is considered. Comparedwith the existing result, a more general switching control methodis proposed to guarantee the quadratic stabilization. This switchingcontrol method is based on the partition of the vertex matrixset of each subsystem. By this method, the matrix inequalitiesneeded to be solved are always less than those needed to besolved before except one extreme case; for this case, it isequal. The switched control synthesis problem is also studiedfor both switched state feedback and output feedback. Severalbilinear matrix inequality based conditions are derived forboth cases.     

Robust finite-time H∞ control of singular stochastic systems via static output feedback

This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H_∞ finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H_∞ finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.     

The guaranteed cost control for uncertain nonlinear large-scale stochastic systems via state and static output feedback

The guaranteed cost control (GCC) problem involved in decentralized robust control of a class of uncertain nonlinear large-scale stochastic systems with high-order interconnections is considered. After determining the appropriate conditions for the stochastic GCC controller, a class of decentralized local state feedback controllers is derived using the linear matrix inequality (LMI). The extension of the result of the study to the static output feedback control problem is discussed by considering the Karush-Kuhn-Tucker (KKT) conditions. The efficiency of the proposed design method is demonstrated on the basis of simulation results.     

Optimal LMI‐based state feedback stabilizer for uncertain nonlinear systems with time‐Varying uncertainties and disturbances

This article presents a nonlinear state feedback stabilizer using linear matrix inequalities for a class of uncertain nonlinear systems with Lipschitz nonlinearities. The proposed controller improves the transient performance and steady state accuracy simultaneously. To improve the stabilization performance, a nonlinear function is included in the control law and is optimally tuned using a modified random search algorithm. Simulation results are presented to show the effectiveness of the offered method. © 2015 Wiley Periodicals, Inc. Complexity 21: 356–362, 2016     

Stabilization problem of stochastic time-varying coupled systems with time delay and feedback control

The stabilization of stochastic coupled systems with time delay and time-varying coupling structure (SCSTT) via feedback control is investigated. We generalize systems with constant coupling structure to the time-varying coupling structure. Combining the graph theory with the Lyapunov method, a systematic method is provided to construct a Lyapunov function for SCSTT, and a Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilization in the sense of pth moment exponential stability. Furthermore, theoretical results are applied to analyze the stabilization of stochastic-coupled oscillators with time delay and time-varying coupling structure in order to illustrate the practicability of the results. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of theoretical results.     

Robust H{infty} dynamic output feedback control for 2D linear parameter-varying systems

James Lam Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong Changhong Wang Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, People's Republic of China Corresponding author. Email: ligangwu{at}hit.edu.cn Email: james.lam{at}hku.hk Email: cwang{at}hit.edu.cn Received on June 28, 2006; Accepted on October 1, 2007 This paper is concerned with the problem of robust dynamicoutput feedback control for 2D discrete-time linear parameter-varyingsystems. Given a Fornasini–Marchesini local state-spacesystem with linear varying parameters, our attention is focussedon the design of full-order dynamic output feedback controller,which guarantees the closed-loop system to be asymptoticallystable and has a prescribed disturbance attenuation performance.A sufficient condition for the existence of a desired robustoutput feedback controller is established in terms of parameterizedlinear matrix inequalities, and the corresponding controllersynthesis is cast into a convex optimization problem which canbe efficiently handled by using standard numerical software.A numerical example is provided to illustrate the effectivenessof the proposed design method.     

Necessary and sufficient conditions for parameter insensitive disturbance-rejection problems with dynamic output feedback

Email: otsuka{at}j.dendai.ac.jp Received on November 11, 2005; Accepted on December 16, 2006 In this paper, necessary and sufficient conditions for the parameterinsensitive disturbance-rejection problem with dynamic outputfeedback which was studied in Otsuka (1999) to be solvable aregiven for the structured uncertain linear systems. Further,necessary and sufficient conditions for the solvability of theproblems with static output feedback and state feedback arealso studied as special cases. The obtained results containsome extensions of the previous results to the structured uncertainlinear systems.