Discontinuous integro-differential equations and sliding mode control

The paper deals with analysis and design of sliding mode control systems modeled by finite-dimensional integro-differential equations. Filippov method and equivalent control approach are extended to a class of nonlinear discontinuous integro-differential equations and to a class of control systems modeled by infinite-dimensional differential equations in Banach spaces. Sliding mode control algorithms are designed for distributed input delay systems and for a heat control system.