Piecewise Linear System Control Study

The analysis and design of piecewise linear systems is the main contents of this paper.Piecewise linear systems constitute a special class of nonlinear systems and arise often in practical control systems when piecewise linear components are encountered. In addition, many other classes of nonlinear systems can also be approximated by the piecewise linear systems.Based on a piecewise quadratic Lyapunov function, this paper presented a stability analysis and optimal controller design method for piecewise linear systems. It is shown that the closed loop system is globally stable with guaranteed cost or L₂ gain performance and the control law can be obtained by solving a set of Linear Matrix Inequalities that is numerically feasible with commercially available software.Piecewise linear systems may exhibit sliding modes on the boundaries between two or more cells. This paper proposed a method based on the sliding mode variable structure control theory to design a stability controller for a class of piecewise second dimension linear systems, which produce sliding modes upon the boundaries and control the sliding to move with expected direction.