ABSTRACT. The paper deals with the time switching hybrid systems described by nonlinear control equations with nonlinearity of a sector form. The estimation of the solution of the control system at any moment is established through the method of Lyapunov function. Both cases, stable and unstable control systems are considered. The final estimation of the solution of the hybrid system is obtained from the composition of perturbations of the separate control systems using the condition of solution continuity in the points of switching.

In this paper we propose a nonlinear controller based on sum of squares decomposition applied to turbocharged diesel engine. The basic idea is to employ polynomial Lyapunov function in order to formulate the stability sufficient condition in the terms of state dependent matrix inequalities. The obtained controller gain guarantees the global convergence of the system and regulates the flows for the Variable Geometry Turbocharger and the Exhaust Gas Recirculation systems in order to minimize the NO x emission and the smoke of diesel engine. Simulation of the control performances through a professional software shows the effectiveness of this approach.

In this paper, we propose a Control Lyapunov Function based nonlinear robust controller for turbocharged Diesel engine. The basic idea is to develop inverse optimal control and utilize more general Lyapunov function which provides additional degree of freedom in order to achieve better performance. The obtained controller gain guarantees the global convergence of the Diesel engine system and regulates the flows for the Variable Geometry Turbocharger and Exhaust Gas Recirculation systems in order to optimize oxygen-fuel ratio and intake manifold EGR fraction. Simulation of the control performance based on professional simulator AMESim (LMS) shows the effectiveness of this approach.

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