Bounded control theory

A fundamental problem in control systems theory is that stability is not always guaranteed for a closed-loop system even if the plant is open-loop stable. With the only knowledge of the input-to-state (practical) stability (ISpS) of the plant, a bounded integral controller (BIC) has been developed which generates a bounded control output independently from the plant parameters and states and guarantees closed-loop system stability in the sense of boundedness. This concept has been further extended to ensure state-limitation for a wide class of nonlinear systems, resulting in the design of the state-limiting PID controller that has been effectively applied in several engineering systems including power converters and electrical drives.