A 2-D systems approach to river pollution modelling
Multidimensional Systems and Signal Processing
Multi-time Euler-Lagrange dynamics
ISTASC'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Systems Theory and Scientific Computation - Volume 7
Multitime models of optimal growth
WSEAS Transactions on Mathematics
A solution to the continuous and discrete-time linear quadratic optimal problems
WSEAS Transactions on Systems and Control
Control for stability and positivity of 2-D linear discrete-time systems
WSEAS Transactions on Systems and Control
Robust stability analysis for 2-D continuous-time systems via parameter-dependent Lyapunov functions
WSEAS Transactions on Systems and Control
Necessary and sufficient conditions of reachability for a model of multidimensional hybrid systems
ISTASC'08 Proceedings of the 8th conference on Systems theory and scientific computation
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A class of multidimensional hybrid linear systems is presented, with the time vector composed by q continuous-time real components and by r discrete-time integer ones, q, r ≥ 1. The state equation is of multidimensional partial differential-difference type. A generalized variation-of-parameters formula is provided and it is used to obtain the state and the general response of the system. The fundamental concept of observability is studied for these systems. An observability Gramian is introduced, which is a generalization of the Gramians corresponding to the classical 1D continuous-time and 1D discrete-time systems. In the case of completely observable systems this Gramian is used to obtain a formula which provides the initial state of the system for any input-output pair. A list of observability criteria is given for time-invariant systems and the duality between the concepts of observability and reachability is emphasized.