Peddapullaiah Sannuti

Simultaneous internal and external stabilization of linear time-invariant systems in the presence of constraints is pursued. Internal stabilization is in the sense of Lyapunov while external stabilization is in the sense of L_p l_p stability with different variations, e.g. with or without finite gain, with fixed or arbitrary initial conditions, with or without bias. Concept of Lyapunov stability is well known. External stability seeks the controlled output be in L_p or l_p space for p = 1 to infinity whenever the external input or disturbance d of a system is in L_p or _p space. Several simultaneous external and internal stabilization problems are studied in depth, and appropriate adaptive feedback controllers that achieve the intended simultaneous external and internal stabilization are constructed whenever such problems are solvable.

Constraints can appear in many forms. They manifest in the form of imposing certain inputs or state variables be within certain bounded regions in their respective spaces. For instance, most nonlinear systems encountered in practice consist of linear systems and static nonlinear elements. Saturation is a ubiquitous non-linearity.

Physical quantities such as speed, acceleration, pressure, flow, current, voltage, and so on, are always limited to a finite range, and saturation non-linearities are therefore a ubiquitous feature of physical systems.