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The singular linear-quadratic optimal control problem for a class of discrete-time linear singular systems with multiple time-delays is investigated. The equivalent relationship between this problem and the non-singular linear-quadratic problem for standard state-space discrete-time linear systems without time-delay is derived, and the necessary and sufficient condition guaranteeing this equivalent relationship is also given. The optimal control is synthesized as state feedback, and the closed-loop system is regular, impulse-free and without time-delay. An example is given to show the validity of the proposed method.

This paper discusses the output regulation problem of the disturbed singular systems. The relation between this problem and the output regulation problem of standard state-space linear systems is given based on the Weierstrass canonical form of singular systems. For the case of that the disturbance is described by differential equation, the sufficient and necessary condition of which the output regulation problem is solvable and a way to design corresponding controller are given.

In this paper, the problem of output feedback variable structure control design for multivariable linear singular systems is discussed. An algorithm of switching surface design and stability analysis of sliding mode motion are given, the output feedback variable structure control design and global asymptotic stability analysis of closed-loop are given. The control design given in this paper assures that closed-loop trajectory converges to zero with arbitrary exponent speed.

In this paper, the LQ problem of time-Invariant discrete singular systems Is treated, and the equivalent relationship between the LQ problem of singular systems and that of linear systems Is given by an approach of the artificial feedback. Meanwhile, the exsitence and uniqueness of the optimal control-trajectory pair are obtained, and the expression of the optimal control and its state-feedback synthesis are also derived.

The convergence properties of the LS filtering of the state of linear systems with measurement noise are investigated. The necessary and sufficient conditions for the filter error converging to zero almost surely or in mean square are given and the convergence rates of the filter error are also obtained. As an application of the LS filtering, a new approach to the precise estimate of the periodic disturbances mixed in dynamic systems is proposed.

In this paper, the linear-quadratic optimal regulator of descriptor systems with the terminal state constrained is investigated and the explicit expression for the optimal control is obtained.

The problem of disturbance attenuation is addressed for a class of nonlinear systems with disturbance having bounded L2 norm. By connecting semiglobal Hinfin control with the semiglobal solution of the dissipation inequality, a design procedure for output feedback control laws is presented on the basis of high-gain observer. For any given bounded subset of L2[0, infin] and any given compact subset of state space, the resulting controllers render the L 2 gain between disturbance in the given bounded subset and the output less than the prescribed number, and achieve locally asymptotically stable with the domain of attraction containing the compact subset without disturbance

The problem of decentralized output tracking is addressed for a class of large-scale nonlinear systems. By introducing a new type of high-gain observers and using the recursive procedure, we present a procedure for constructing decentralized output feedback controllers under a Lipschitz condition. The proposed controllers achieve the exponential asymptotic tracking of the given constant reference signals while maintaining internal boundedness. Finally, simulation shows the effectiveness of our result.

The problem of output feedback robust H/sub /spl infin// control is considered for a family of nonlinear systems with dynamic uncertainties at the input of the plant. By introducing a high-gain observer with tow design parameters, a robust output feedback controller is explicitly constructed. The proposed controllers attenuate the disturbance's effect on the output of the closed-loop system to an arbitrary degree of accuracy in the L/sub 2/-gain sense, and achieve global asymptotic stability in the absence of disturbance.

In this paper, the optimal control for regulating linear singularly perturbed systems with perturbed quadratic-cost is presented by discussing the singular quadratic-cost control problem for the reduced-order slow subsystem. Under some assumptions, the optimal performance cost of the singularly perturbed system will tend to that of the reduced-order slow subsystem.

The problem of inputs decoupled observer design for linear descriptor systems with unknown inputs was considered. When the system was impulsively controllable, an equivalent standard state space system was derived by regarding the partial state as unknown input. The sufficient conditions for the existence of the observer and simple method to design the observer are given.

In this paper, the linear quadratic optimal control problem of singular nonlinear systems is considered. The weight matrix of control is not assumed nonsingular. Under some conditions, the problem is equivalently transformed into the optimal control problem of standard state space systems. Some sufficient conditions solving the optimal control problem are given. The optimal control can be synthesized as state feedback and the closed-loop system has a unique state trajectory with the given initial value.

The guaranteed cost control problem via memoryless state feedback is studied in this paper for a class of linear singular time-delay systems with norm-bounded time-varying parametric uncertainty and a given quadratic cost function. First, one sufficient condition for the stability of singular time-delay system is got. Then the sufficient conditions for the existence of guaranteed cost controller are given in terms of linear matrix inequalities (LMIs). Furthermore, one simple example is shown to illustrate the application of the proposed method.

In this paper, the problem of state and input estimation for linear singular systems with unknown inputs is concerned. An equivalent standard state spaces system is derived for the purpose of the observer design. The necessary and sufficient conditions for the existence of, the observer and the simple method to design the observer are given. The robust stability of the closed-loop obtained by dynamic output feedback is also discussed.

A necessary and sufficient condition for the output regulation problem to be solvable by output feedback reduced-order normal controllers is derived, which can be constructed explicitly.

In this paper, exact linearization via state feedback and stabilization for a class of nonlinear differential-algebraic systems are considered. Using a local diffeomorphism and a state feedback, the nonlinear differential-algebraic system is transformed to a linear normal system. Choosing a appropriate feedback controller, the closed-loop system is asymptotically stabilized.

An observer-based stability controller is established for linear systems with delay in state. The controller not only realizes the separation of characteristic roots for the closed-loop system, but also makes the closed-loop transfer function equal to the transfer function of closed-loop constructed directly by state feedback. Using the separation of characteristic roots, the stability condition is presented. The controller can be obtained by solving two linear matrix inequalities (LMIs). Two illustrative examples are given to show the applicability of the proposed approach.

In this paper, the singular LQ problem for descriptor systems is discussed. Under some general assumptions, the optimal control synthesized as state feedback is obtained and the closed-loop system is regular, impulse-free and stable.

In this paper the optimal consumption-tracking problem of the singular dynamic input-output macro-economic model is solved by using a new method called artificial feedback technique. Here, the objective functional is chosen as the LQ cost based on a consumption-tracking principle, and the system equation is described as a singular linear difference equation with a non-regular pencil of matrices. >

The LO problem of multiple valued discrete time varying singular systems is discussed. The equivalent relation between this problem and that of standard state space systems is given via an approach of the artificial feedback under some conditions. The existence and uniqueness of the optimal control trajectory pair are obtained. The state feedback synthesis of the optimal control law is also derived and the optimal closed loop system is just single valued. >

In this paper, the optimal regulation of continuous time-varying linear singular systems with quadratic cost including crossterms is discussed. The existence and uniqueness of the optimal control-trajectory pair is proved. Further the solution of this problem is presented and an optimal feedback control law is provided.