A new method for the design of reduced-order observers for descriptor systems with unknown inputs is presented. The approach is based on the generalized constrained Sylvester equation. Sufficient conditions for the existence of the observer are given.

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Reduced-order observer design for descriptor systems with unknown inputs

Two detectability notions are introduced for the most general class of linear descriptor systems. Necessary and sufficient conditions are derived for the detectabilities and for the existence of observers. Depending on existence conditions satisfied, the observers can be either in the familiar Luenberger form or in a generalized form, i.e., in descriptor form as the original system itself is. A unified procedure is provided for the design of observers in both forms.

Observer design for descriptor systems

A design approach for observers using multiple-integrals is presented for descriptor systems, which allows the authors to decouple or attenuate measurement output disturbances. Design schemes for both pure integral observers and proportional integral observers are investigated. Measurement noise and input disturbances are also simultaneously taken into account in the design. A systematic design procedure for a causal or normal multiple-integral observer is addressed, which can be implemented conveniently using Matlab software. The considered disturbance may be unbounded, which means that the presented design approach is suitable for more general cases. Moreover, the system state, together with the disturbance vector and its finite time derivatives can be simultaneously estimated. The proposed design has great potential for application to control problems, such as those in diagnosis or observer-based control. In addition, it also has good estimation robustness and can be directly applied to normal systems. Simulation results show a satisfactory tracking performance as compared to the results obtained for descriptor systems.

Proportional multiple-integral observer design for descriptor systems with measurement output disturbances

A new approach to the design of a class of Luenberger observers for descriptor systems is presented. The design is performed in a straightforward manner. The conditions required in the design are given in terms of the original system matrices. The relationship among these and other well-known conditions is highlighted. >

Design of a class of Luenberger observers for descriptor systems

In this paper, we study average consensus problem in networks of dynamic agents with uncertain topologies as well as time-varying communication delays. By using the linear matrix inequality method, we establish several sufficient conditions for average consensus in the existence of both uncertainties and delays. Several linear matrix inequality conditions are presented to determine the allowable upper bounds of time-varying communication delays and uncertainties. Numerical examples are worked out to illustrate the theoretical results.

Average consensus in networks of dynamic agents with uncertain topologies and time-varying delays

Observer design for generalized state space systems with unknown inputs

Frequency-domain conditions for disturbance rejection and decoupling with stability or pole placement

Disturbance rejection of left-invertible systems

The problem of independent force and position control of multitask cooperating manipulators is studied. Each manipulator is in a non-singular configuration and the object can be driven by the contact forces exerted by the end effectors of the manipulators. The design requirement is to control each coordinate of the position of the object as well as each component of the “rest” forces, except the moving forces that are determined uniquely from the object's position. The present design requirement has been proved to be always satisfied together with asymptotic and BIBO stability. A class of controllers solving the above simultaneous problem is analytically determined. The proposed state feedback controller does not depend upon the specific object dynamics and thus the resulting closed-loop multimanipulator system performs as required, not only when handling various objects but also when the dynamics of the objects are unknown or hard to compute or disturbed by external forces.

Independent force and position control for cooperating manipulators

The important transfer function design problems of input-output decoupling, exact model matching and disturbance rejection, via static measurement output feedback, are studied for the case of generalized state space systems. Necessary and sufficient conditions for the solvability of these problems are established. The general analytical expressions of the respective controller matrices are derived. The above results are also extended to cover the combined problem of disturbance rejection with simultaneous decoupling and the problem of disturbance rejection with simultaneous exact model matching.

K. G. Tzierakis

Papers

Observer design for generalized state space systems with unknown inputs

Frequency-domain conditions for disturbance rejection and decoupling with stability or pole placement

Disturbance rejection of left-invertible systems

Independent force and position control for cooperating manipulators

Meeting transfer function requirements via static measurement output feedback