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Ideal observability for bilinear discrete-time systems with and without delays in observation

Lhous M., Rachik M., Magri E. M.

Archives of Control Sciences

2018

Vol. 28, No. 4

601--616

An ideal observability subspace expression is stated for bilinear abstract system with bounded operator in Hilbert spaces. The case of finite dimentional space is also treated. However, it’s noticed that the state ideal observability can never be fulfilled within an infinite dimensional phase space in the case of scalar output. The case of bilinear discrete-time system with delays in observation is also described. To illustrate this work some examples are presented.

Discrete-time Markovian jump linear systems

Szajowski K., Koning W.

Control and Cybernetics

1998

Vol. 27, no 1

63-80

The paper considers a problem of optimal control of a linear system with the parameters dependent on the states of a Markov chain. The cost criterion is quadratic in the controls and states of the system. The criterion parameters also depend on the states of the Markov chain. Two models of observation of the Markov chain are adopted - delay for one step and no delay. It is shown that under appopriate mean square detectability and stabilizability conditions the infinite horizon optimal control problem for the general case of Markovian jump linear quadratic systems has a unigue mean square stabilizing solution. Necessary and sufficient conditions are given to determine if a system is mean square stabilizable.