Piecewise linear control modeling and analysis with applications in circuits and automotive systems

This research addresses the analysis and nonlinear control design of piecewise linearizied system models of multiple input multiple output control systems. The nonlinear state equations are mapped using piecewise linear theory and extended to investigate the challenging dynamic behavior of practical systems. Also the equations are copied to model a complex-nonlinear circuit in which the outputs plotted and compared to analogous mechanical model of the same system to give a more intuitive understanding of the control process. The dynamics of the system calculated using explicit analytical formulas, as by using numerical integration. The state equations are also modeled in SIMULINK (k) and Maple and compared to their physical realizations and measurements. The closed form solution for the state flow is given by sets of equations in the first examples are representing the solutions of the linear parts of system, each valid in its respective region defined by the boundaries of the piecewise linear function. The state transition from one domain to another also occurs whenever the trajectory crosses one of the planes of the piecewise linear function in an automotive engine model where a circuit analog is applied via LQR and Lyapunov control function to achieve desirable dynamic behavior.