Global regulation of null-controllable input-saturated systems with arbitrary l2 state disturbances

This paper presents a globally stabilizing control strategy for LTI asymptotically null-controllable with bounded-inputs (ANCBI) discrete-time linear systems in the presence of input-saturation and arbitrary l₂ state disturbances. The class of linear ANCBI plants consists of all dynamic linear systems without exponentially unstable modes. The method is based on the solution, at each time instant, of a generalized algebraic Riccati equation which arises in minimax control theory. The resulting time-varying control action consists of a linear piecewise-constant state-feedback control law which becomes constant by a finite, possibly large, disturbance-depending time. Monotonicity properties of suboptimal H_∞ or minimax control are established and exploited so as to develop a suitable state-dependent feedback selection logic for regulating input-saturated linear plants in the presence of l₂-disturbances