# Download Bilinear Control Processes: With Applications to by Ronald R. Mohler PDF

By Ronald R. Mohler

Similar information theory books

Information theory: structural models for qualitative data

Krippendorff introduces social scientists to details concept and explains its software for structural modeling. He discusses key themes similar to: find out how to make certain a knowledge concept version; its use in exploratory learn; and the way it compares with different techniques corresponding to community research, course research, chi sq. and research of variance.

Ours To Hack and To Own: The Rise of Platform Cooperativism, a New Vision for the Future of Work and a Fairer Internet

The on-demand financial system is reversing the rights and protections employees fought for hundreds of years to win. traditional web clients, in the meantime, keep little keep an eye on over their own info. whereas promising to be the nice equalizers, on-line systems have frequently exacerbated social inequalities. Can the net be owned and ruled otherwise?

Additional info for Bilinear Control Processes: With Applications to Engineering, Ecology, and Medicine

Example text

For example, the reachable zone from the pointy is just the shaded region. A bilinear system is completely controllable if the conditions given by the main result are satisfied. As one might expect, the conditions are not as simple as the popular conditions for complete controllability of linear systems with unconstrained control or for null controllability with constrained control. For phase-variable systems, however, the sufficient conditions are easy to apply. In practice, a bilinear mode may be implemented by controlling significant plant parameters in a manner similar to the variable wing geometry of high-performance aircraft.

4 EQUILIBRIUM SET OF BILINEAR S Y S T E M S Here, the set of equilibrium points is described for bilinear systems. This description is necessary to understand the connectedness property that is utilized to show complete controllability. 14) if the indicated inverse matrix exists. If the system matrix is singular for a control value u = a, no equilibrium state exists corresponding to ii unless Cii happens to lie in the range of A ErzlUkBk, in which case an infinite number of states are equilibrium states.

29) can take on either positive or negative values, and it follows that L(x) is just the linear subspace spanned by (Bkx + ck), k = 1,2,. , m. 29) are constrained to be only positive or only negative. 28) exists, {k(x, u) I u E U} is a closed convex set which does not contain the origin; hence it is contained in the interior of some half-space whose bounding hyperplane passes through the origin. In this case x is not an equilibrium point of the system, and all rays of L(x) point into the interior of the half-space above.