This paper considers a hybrid approach to control of linear dynamic and impulse controllable continuous-time disturbed linear descriptor systems. The first step in control is a design of continuous state feedback that makes system impulsefree. The obtained system is represented as a state space system of relative order zero. Based on this model, a full order discretetime sliding mode control providing given pole placement is designed. The reaching control is completely decentralized and chattering-free. Simulations show a very good suppression of slow disturbances. All design steps and simulations require only standard MATLAB Toolbox.
I. INTRODUCTIONHE main characteristic of continuous-time (CT) linear descriptor models is that the derivative of coordinate x cannot be calculated from control inputs and their present values. These models either mirror reality of a system, or are an intentional result of modeling. Linear electric circuits, for example, have descriptor models, as well as mechanical systems with mass matrix practically singular. Sometimes the design of the mechanical subsystem is a descriptor, as e.g. robot window washer. Singular model arises when outputs of state space sub-systems are inputs to other state space subsystems, making a large complex system. The descriptor systems are more complicated than regular state-space systems and they require separate methods for control synthesis. Detailed presentation of differences between regular state-space systems and descriptor (or singular) systems are given in [1].The properties and design control methods (mostly linear) of descriptor systems are well covered in publications [2]- [5]. Recently published book [6] extensively covers properties of descriptor systems and methods of their analysis and control design. Design methods are concentrated to desired dynamics, impulse elimination and regularization, while the disturbance effects are rarely considered.