Sliding mode control in infinite-dimensional systems (Q1113856)

An infinite-dimensional control system in Banach spaces, given by \(\dot x=Ax+bu(x,t)+f,\) is considered. Here the control u undergoes discontinuities on the surface \(Cx=0\), where C is a linear operator. The equivalent control method is applied and a theorem on the convergence of the sliding mode is obtained. An application to the control of a multi- dimensional heat process is presented.