a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

A new approach to robust ltering, prediction and smoothing of discrete-time signal vectors is presented. Linear time-invariant lters are designed to be insensitive to spectral uncertainty in signal models. The goal is to obtain a simple design method, leading to lters which are not overly conservative. Modelling errors are described by sets of models, parameterized by random variables with know...

In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus+innovations distributed linear estimator of the dynamic field termed as Consensus+Innovation...

This paper addresses the problem of H∞ filtering for discrete-time linear systems with Markovian jumping parameters. The main contribution of the paper is to provide a linear matrix inequality approach for designing an asymptotically stable linear time-invariant H∞ filter for systems where the jumping parameter is not accessible. The cases where the transition probability matrix of the Markov c...

Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...

This paper addresses the stabilization problem for single-input Markov jump linear systems via modedependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and amode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results fo...