M.G. Kabuli

Reliable decentralized control

We study reliable stabilization of linear, time-invariant, multi-input multi-output, two-channel decentralized control systems. We develop necessary and sufficient conditions for reliable decentralized stabilizability under sensor or actuator failures and present reliable decentralized controller design methods for strongly stabilizable plants.

Reliable decentralized integral-action controller design

Reliable stabilizing controller design with integral-action is considered for linear time-invariant, multi-input-multi-output decentralized systems with stable plants. Design methods are proposed to achieve reliable closed-loop stability with integral-action in each output channel for asymptotic tracking of step-input references applied at each input. The design approaches guarantee stability and integral-action in the active channels when all controllers are operational and when any of the controllers is set equal to zero due to failure.

Parametrization of stabilizing controllers with integral action

In the standard linear time-invariant multi-input/multi-output unity-feedback system, a parametrization of stabilizing controllers with integral action is obtained. These controllers guarantee asymptotic tracking of step reference inputs at each output channel with zero steady-state error.

Reliable stabilization with integral action in decentralized control systems

Reliable stabilization with integral action is studied in the linear, time-invariant, multi-input, multi-output, two-channel decentralized control system, where the plant is stable. The objective is to achieve closed-loop stability when both controllers act together and when each controller acts alone. Necessary and sufficient conditions are obtained for existence of block-diagonal decentralized controllers that ensure reliable stabilization and integral action. All decentralized controllers with integral action that provide reliable stabilization are characterized.

Conditions for stability of feedback systems under sensor failures

An examination is made of the closed-loop stability of the unity-feedback system under two classes of sensor connection failures. The actuator-failure case is similar and omitted for brevity. If there exist compensators that R/sub U/-stabilize the given plant for all failures in these classes, where R/sub U/ denotes a ring of proper scalar rational functions, then the denominator matrices of coprime factorizations of the plant must satisfy certain conditions. A set of compensators that R/sub U/-stabilize a class of multi-input, multi-output plants under sensor failures is found.<<ETX>>

Nonlinear plants, factorizations and stable feedback systems

For nonlinear plants represented by causal maps defined over extended spaces, right factorization and normalized right-coprime factorization concepts are discussed in terms of well-posed stable feedback systems.

Feedback stabilization of a class of nonlinear plants using a factorization approach

The authors generalize the right-coprimeness definition by requiring only that the corresponding plants pseudo-state be reconstructable by a two-input one-output stable observer. They obtain right-coprime factorizations for a class of nonlinear plants for which a two-input one-output pseudo-state observer is constructed. A feedback stabilization scheme is given using this observer.<<ETX>>

Stabilization of linear systems under nonlinear stable diagonal perturbations

Stability of linear, time-invariant, multi-input multi-output unity-feedback systems is considered under nonlinear, time-varying, stable perturbations. Necessary and sufficient conditions are obtained for stability of the perturbed system and specialized for the case of one arbitrary failure whose location is unknown. Controller design methods are developed ensuring stability under an unknown stable failure of at most one arbitrary sensor or actuator. >

Simultaneous stabilization of linear systems under stable additive or feedback perturbations

In the standard linear, time-invariant, multi-input multi-output unity-feedback system, it is shown that a given plant and one obtained by a known stable additive (or feedback) perturbation of this plant can be simultaneously stabilized by a common controller. The plant is not necessarily stable. No small-gain restrictions are imposed on the stable perturbations. A set of simultaneously stabilizing controllers is explicitly derived for any such pairs of plants. The results extend the standard single connected set of plants description in robust control design methods to two (possibly disjoint) sets of plants. >

Simple parametrization of controllers with integral action

A parametrization of stabilizing controllers with integral action is obtained in the the standard linear time-invariant, multi-input-multi-output (MIMO) unity-feedback system. These controllers guarantee asymptotic tracking of step reference inputs at each output channel with zero steady-state error.