Internal stabilization and external Lp stabilization of linear systems subject to constraints

Having studied during the last decade several aspects of several control design problems for linear systems subject to magnitude and rate constraints on control variables, during the last two years the research has broadened to include magnitude constraints on control variables as well as state variables. Recent work by Han et al. (2000), Hou et al. (1998) and Saberi et al. (2002) considered linear systems in a general framework for constraints including both input magnitude constraints as well as state magnitude constraints. In particular, Saberi et al. consider internal stabilization while Han et al. consider output regulation in different frameworks, namely a global, semiglobal, and regional framework. These problems require very strong solvability conditions. Therefore, a main focus for future research should focus on finding a controller with a large domain of attraction and some good rejection properties for disturbances restricted to some bounded set.