Minimum Energy Control of Descriptor Fractional Discrete–Time Linear Systems with Two Different Fractional Orders

Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass–Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.

New Sliding Mode Controller Based on Second Order Reachability Law

Sliding mode control systems provide robust and simple means for controlling linear and nonlinear plants whose parameters may vary within known boundaries. The existence of an ideal sliding mode requires fast switching, which induces chattering in the system, may excite high frequency plant dynamics and consequently affect the stability of the system. This paper proposes a new simple sliding mode controller based on second order reachability law. The reachability condition in this paper is based not only on the first derivative of the switching function but also on its second derivative. The proposed controller alleviates chattering, guarantees zero steady state error, and offers smooth transients for the system states. To demonstrate the validity of the proposed controller, a second order system is used as a workbench example. The simulation results of the workbench example using MATLAB illustrate the feasibility and efficacy of the proposed controller.