@conference {
	title = {Almost Sure Convergence to Consensus in Markovian Random Graphs},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {12/2008},
	abstract = {In this paper, we discuss the consensus problem for a network of dynamic agents with undirected information flow and random switching topologies. The switching is determined by a Markov chain, each topology corresponding to a state of the Markov chain. We show that in order to achieve consensus almost surely and from any initial state the sets of graphs corresponding to the closed positive recurrent sets of the Markov chain must be jointly connected. The analysis relies on tools from matrix theory, Markovian jump linear systems theory and random processes theory. The distinctive feature of this work is addressing the consensus problem with {\textquotedblleft}Markovian switching{\textquotedblright} topologies.},
	address = {Cancun, Mexico},
	booktitle = {47th IEEE Conference on Decision and Control},
	pages = {pp. 3535-3540}
}
@conference {
	title = {Optimal Linear Quadratic Regulator for Markovian Jump Linear Systems, in the Presence of One Stop-Time Step Delayed Mode Observations},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {07/2008},
	abstract = {In this paper, we provide the solution to the optimal Linear Quadratic Regulator (LQR) paradigm for Markovian Jump linear Systems, when the continuous state is available at the controller instantaneously, but the mode is available only after a delay of one-time step. This paper is the first to investigate the LQR paradigm in the presence of such mismatch between the delay in observing the mode and the continuous state at the controller. We show that the optimal LQR policy is a time-varying matrix gain multiplied by the continuous component of the state, where the gain is indexed in time by the one-step delayed mode. The solution to the LQR is expressed as a collection of coupled Riccati iterations and equations, for the finite and the infinite horizon cases respectively. In the infinite horizon case, the solution of the coupled Riccati equations or a certificate of infeasibility is obtained by solving a set of linear matrix inequalities. We also explain the difficulties of solving the LQR problem when the mode is observed by the controller with a delay of more than one step. We show that, with delays of more than one time-step, the optimal control will be a time-varying nonlinear function of the continuous state and of the control input, without presenting an exact solution.},
	address = {Seoul, Korea},
	booktitle = {17th IFAC World Congress},
	pages = {pp. 8056-8061}
}
@conference {
	title = {Optimal State Estimation for Discrete-Time Markovian Jump Linear Systems, in the Presence of Delayed Mode Observations},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {06/2008},
	abstract = {In this paper, we investigate an optimal state estimation problem for Markovian Jump Linear Systems. We consider that the state has two components: the first component of the state is finite-valued and is denoted as mode, while the second (continuous) component is in a finite dimensional Euclidean space. The continuous state is driven by a deterministic control input and a zero mean, white and Gaussian process noise. The observable output has two components: the first is the mode delayed by a fixed amount and the second is a linear combination of the continuous state observed in zero mean white Gaussian noise. Our paradigm is to design optimal estimators for the current state, given the current output observation. We provide a solution to this paradigm by giving a recursive estimator of the continuous state, in the minimum mean square sense, and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditional on the observed output. We show that the optimal estimator is nonlinear on the observed output and on the control input. In addition, we show that the computation complexity of our recursive schemes is an exponential function of the mode observation delay.},
	address = {Seattle, Washington},
	booktitle = {2008 Automatic Control Conference},
	pages = {pp.  3560-3565}
}
@conference {
	title = {Optimal State Estimation for Discrete-Time Markovian Jump Linear Systems, in the Presence of Delayed Output Observations},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {05/2008},
	abstract = {In this paper, we investigate the design of optimal state estimators for Markovian Jump Linear Systems. We consider that the state has two components: the first component is finite-valued and is denoted as mode, while the second (continuous) component is in a finite dimensional Euclidean space. The continuous state is driven by a zero mean, white and Gaussian process noise. The observation output has two components: the first is the mode and the second is a linear combination of the continuous state observed and zero mean white Gaussian noise. Both output components are affected by delays, not necessarily equal. Our paradigm is to design optimal estimators for the current state, given the current output observation. We provide a solution to this paradigm by giving a recursive estimator for the continuous state, in the minimum mean square sense, and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditioned on the observed output. We show that when the mode is observed with a greater delay than the continuous output component, the optimal estimator nonlinear in the observed outputs.},
	address = {Porto, Portugal},
	booktitle = {IEEE Information Theory Workshop (ITW 2008)},
	pages = {pp. 237-242}
}
