Overlapping guaranteed cost control for uncertain continuous-time delayed systems

Overlapping guaranteed cost control design problem is solved for a class of linear continuous-time uncertain systems with state as well as control delays. Unknown arbitrarily time-varying uncertainties with known bounds are considered. A point delay is supposed. Conditions preserving closed-loop systems expansion-contraction relations including the identical bounds of performance indices are proved. A linear matrix inequality (LMI) delay independent procedure is used for control design in the expanded space. The results are specialized on the overlapping decentralized control design. A numerical illustrative example is supplied.Peer ReviewedPostprint (published version

Controllability-observability of expanded composite systems

The relation between original and expanded systems within the Inclusion Principle from the point of view of controllability–observability of both subsystems and composite systems is studied. It is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable–observable. Two practically important large classes of complementary matrices are identified to offer results computationally attractive. First, the existence of complementary matrices ensuring controllability–observability of decoupled subsystems is proved. Then, using this result, the same property is proved for the composite expanded system.Peer ReviewedPostprint (published version

Preservation of controllability-observability in expanded systems

The result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is suppliedPeer ReviewedPostprint (published version

Overlapping controllers for uncertain delay continuous-time systems

Diploma de l’Institute of Information Theory and Automation Academy of Sciences of the Czech Republic.This papers extends the Inclusion Principle to a class of linear continuous-time uncertain systems with state as well as control delays. The derived expansion-contraction relations include norm bounded arbitrarily time-varying real uncertainties and a point delay. They are easily applicable also to polytopic uncertainties. These structural conditions are further specialized on closed-loop systems with arbitrarily time-varying parameters, a point delay, and guaranteed quadratic costs. A linear matrix inequality (LMI) delay independent procedure is used for control design in the expanded space. The results are specialized on the overlapping decentralized control design. A numerical illustrative example is supplied.Peer ReviewedAward-winnin

Overlapping LQ control of discrete-time time-varying systems

Overlapping decentralized linear quadratic control design problem for discrete-time time-varying systems is solved by using generalized selection of complementary matrices. Explicit conditions on the structure of complementary matrices are derived, including conditions on contractability of controllers. Systematic procedure for their selection is given.Peer Reviewe

Overlapping guaranteed cost control for time-varying discrete-time uncertain systems

© 2002 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The paper presents results on the inclusion principle for uncertain, nominally linear, time-varying, discrete-time systems. The systems under consideration have time-varying norm-bounded parameter uncertainties in both state and input matrices. Robust controllers are assumed to be available by using guaranteed cost control approach. The main contribution is in the derivation of explicit block structured conditions on complementary matrices of systems and controllers within the expansion-contraction scheme. A particular selection procedure for complementary matrices is included

Overlapping resilient H2 filtering for uncertain continuous time systems

© 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The paper presents the expansion-contraction relations within the inclusion principle for a class of continuous- time uncertain systems when considering H2 filtering with additive filter uncertainty. Norm bounded uncertainties are considered. The main contribution is the derivation of conditions under which a resilient filter designed in the expanded space is contracted into the initial system preserving simultaneously optimized upper bound for the error variance. An LMI procedure is supplied for resilient full order robust minimum variance filter design. The results are specialized into the overlapping decentralized filter setting. It enables to construct robust resilient H2 filters with block tridiagonal gain matrices.Peer Reviewe

Overlapping guaranteed cost control for uncertain discrete-time systems

Robust overlapping guaranteed cost control problem is presented for a class of state-delayed discrete-time systems. Unknown arbitrarily time-varying uncertainties with given known bounds are considered. Conditions preserving closed-loop systems expansion-contraction relations including the equality of bounds of costs are proved. A linear matrix inequality (LMI) delay independent approach is used for control design in the expanded space. The results are specialized on the overlapping decentralized control design. A numerical illustrative example is supplied.Peer Reviewe

Overlapping quadratic optimal control of linear time-varying commutative systems

© 2002 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Overlapping quadratic optimal control of linear time-invariant continuous-time systems by using generalized selection of complementary matrices has been recently developed as a powerful and effective mean for decentralized control design of linear time-invariant systems. In this paper, it is shown that similar generalizations exist for linear time-varying systems. The results presented here concern implicit conditions for a general form of the transition matrices and explicit conditions for a commutative class of linear time-varying systems.Peer Reviewe

Generalized selection of complementary matrices in the inclusion principle

This paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state LQ optimal control of LTI systems, it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices, the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control designPeer Reviewe