RobustH^∞control of a nonlinear uncertain system via a stable nonlinear output feedback controller

Robust H ∞ control via a stable decentralized nonlinear output feedback controller

“…We wish to synthesize a stable decentralized nonlinear controller for the large‐scale nonlinear uncertain system , , based on the results in . In this case, it is assumed that the large‐scale nonlinear uncertain system , , consists of p interconnected subsystems.…”

“…The nonlinear error systems are considered as additional uncertainties used to form an equivalent nonlinear uncertain system for which a stable nondecentralized nonlinear robust H ∞ controller of the form , is constructed. Here, the nonlinear error systems are required to be absolutely stable. Applying the results in to synthesize the stable nondecentralized nonlinear controller described in Step 1, we first solve a state feedback control problem for the equivalent nonlinear uncertain system. The resulting state feedback gain matrix is then used to guarantee the stability of the nondecentralized nonlinear controller , . Using the state feedback gain matrix obtained from Step 2 and adding an artificial uncertainty, we form an artificial nonlinear uncertain system overbounding the equivalent nonlinear uncertain system formed in Step 1.…”

“…Applying the results in to synthesize the stable nondecentralized nonlinear controller described in Step 1, we first solve a state feedback control problem for the equivalent nonlinear uncertain system. The resulting state feedback gain matrix is then used to guarantee the stability of the nondecentralized nonlinear controller , .…”

“…This allows us to obtain a decentralized nonlinear controller with better performance in attenuating exogenous disturbances as compared with its linear counterpart synthesized using the method in . Such a decentralized nonlinear controller can then be constructed using the same technique as applied in . Here, we incorporate all copies of the nonlinearities back into the system (Figure (b)) to solve the decentralized control problem using the robust H ∞ control method presented in .…”

“…This system is used to synthesize an artificial stable output feedback controller with which we construct the decentralized nonlinear controller. This approach, however, inherently gives rise to some conservatism due to the additional artificial uncertainty .…”