On the detectability and observability of discrete-time Markov jump linear systems

Costa, E.E.; Val, J.B.R. do

doi:10.1109/cdc.2000.914151

Cited by 23 publications

(58 citation statements)

References 10 publications

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“…One can easily check from (7) that the following equivalences hold The next result is adapted from Costa and Fragoso (1993) and do Val and Ba ş ar (1999); see also Costa and do Val (2001).…”

Section: Proofmentioning

confidence: 86%

“…W-detectability is an important and rather general concept introduced in Costa and do Val (2001) that can assure uniqueness and MS-stability of closed-loop solutions of the LQ problem.…”

Section: Discussionmentioning

confidence: 99%

“…Next we present the concepts of weak detectability and weak observability of Costa and do Val (2001). Similarly to Ji and Chizeck (1991 a) we consider the pathwise observability gramian G :…”

Section: Basic Conceptsmentioning

confidence: 99%

“…For instance, we mention the role that mean square stabilizability plays for closed-loop solutions of quadratic in®nite horizon control problems (see Ji et al 1991, Costa andFragoso 1995). Other similarities are presented by the the stochastic concepts of weak detectability (W-detectability) and weak observability (W-observability ) for Markov jump linear systems (MJLS) recently introduced in Costa and do Val (2001), which generalize previous concepts found in the literature and it retrieves the idea that non-observed trajectories are stable in the mean square (MS) sense.…”

Section: Introductionmentioning

confidence: 95%

“…As regards the linear quadratic problem (LQ), it was shown in Costa and do Val (2001) that the W-detectability concept plays the same role of the previous concepts: it assures that the solution to the coupled Riccati equation (CARE) is unique and stabilizing in the MS sense. In spite of the importance of W-detectability in the LQ problem, to this date there is no method of solution to the CARE suitable to systems that are Wdetectable only.…”

Section: Introductionmentioning

confidence: 98%

See 4 more Smart Citations

Weak detectability and the linear-quadratic control problem of discrete-time Markov jump linear systems

Costa¹,

Val²

2002

International Journal of Control

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The paper deals with the stochastic concepts of weak detectability and weak observability for Markov jump linear systems, which is an special class of composite linear systems. The concepts are explored here to strengthen the similarities with the corresponding concepts of deterministic detectability and observability. We introduce a collection of matrices, referred to as the observability matrices. We show that weak observability is equivalent to full rank of each matrix in the set of observability matrices. In addition, we present a stochastic counterpart of the well known result on the invariance of trajectories within non-observable subspaces. These characterizations allow us to clarify the relationship between weak detectability and mean square detectability and to provide a testable condition for weak detectability. Relying on the assumption of weak detectability, we develop a method for solving the linear quadratic problem that is based on iterations of uncoupled algebraic Riccati equations, which converges to the solution of the coupled algebraic Riccati equation if and only if the system is mean-square stabilizable. Numerical examples are included.

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Section: Proofmentioning

confidence: 86%

“…W-detectability is an important and rather general concept introduced in Costa and do Val (2001) that can assure uniqueness and MS-stability of closed-loop solutions of the LQ problem.…”

Section: Discussionmentioning

confidence: 99%

Section: Basic Conceptsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 98%

See 3 more Smart Citations

Weak detectability and the linear-quadratic control problem of discrete-time Markov jump linear systems

Costa¹,

Val²

2002

International Journal of Control

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On Detectability and Observability of Discrete‐Time Stochastic Markov Jump Systems with State‐Dependent Noise

Zhang¹,

Tan²

2013

Asian Journal of Control

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This paper mainly studies the notions of detectability and observability for discrete-time stochastic Markov jump systems with state-dependent noise. Two concepts, called "W-detectability" and "W-observability," for such systems are introduced, and are shown to coincide with the other concepts on detectability and observability reported recently in literature. Moreover, some criteria and interesting properties for both W-detectability and W-observability are obtained.

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Global solutions of a class of discrete‐time backward nonlinear equations on ordered Banach spaces with applications to Riccati equations of stochastic control

Ungureanu

Drăgan

Morozan

2012

Optim Control Appl Methods

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SUMMARYIn this paper, we consider the problem of existence of certain global solutions for general discrete-time backward nonlinear equations, defined on infinite dimensional ordered Banach spaces. This class of nonlinear equations includes as special cases many of the discrete-time Riccati equations arising both in deterministic and stochastic optimal control problems. On the basis of a linear matrix inequalities approach, we give necessary and sufficient conditions for the existence of maximal, stabilizing, and minimal solutions of the considered discrete-time backward nonlinear equations. As an application, we discuss the existence of stabilizing solutions for discrete-time Riccati equations of stochastic control and filtering on Hilbert spaces. The tools provided by this paper show that a wide class of nonlinear equations can be treated in a uniform manner.

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On the detectability and observability of discrete-time Markov jump linear systems

Cited by 23 publications

References 10 publications

Weak detectability and the linear-quadratic control problem of discrete-time Markov jump linear systems

Weak detectability and the linear-quadratic control problem of discrete-time Markov jump linear systems

On Detectability and Observability of Discrete‐Time Stochastic Markov Jump Systems with State‐Dependent Noise

Global solutions of a class of discrete‐time backward nonlinear equations on ordered Banach spaces with applications to Riccati equations of stochastic control

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