chapter  9
28 Pages

Large-Scale Stochastic Control Systems

Stability and Stabilization
WithJ. L. Willems, L. Socha

In classical control system analysis and design studies it is assumed that the output variables are measured and available to the controllers to generate the control inputs. This chapter introduces the mathematical model of the systems under consideration and formulates definitions of stochastic stability and stabilizability. It briefly discusses some results on mean-square and pth-mean stability for a special class of stochastic systems called the solvable systems. The feedback strategy stabilizes the stochastic isolated subsystems. However, Criterion does not prove that the composite system is mean-square asymptotically stable. However, for first-order systems, the condition is necessary and sufficient. Much more conservative conditions are obtained, by estimating upper and lower bounds of the quadratic forms from the largest and smallest eigenvalues. The chapter considers the interconnection of two first-order systems the readers want to analyze stability and stabilizability for noise intensities and interconnections satisfying.