Robust Elastic Control Switching System

Switched systems, as a class of special and important hybrid systems, are currently aninternational leading edge direction of the theory research on hybrid systems. After beingproposed, switched systems have aroused great interests of many researchers in control feldsand made great progress. Many physical phenomena in the real world can be modelledby switched systems. Since many uncertainties in practical engineering and fragility incontrollers are the main reasons to deteriorate the systems performance, the robust resilientcontrol problem has received much attention. The paper mainly makes some theoreticalresearches in terms of the robust resilient control problem of switched systems. The cardinalcontents of this article include the following three parts:1) Robust resilient guaranteed cost control for singular impulsive switched systems withtime-varying delayFor singular impulsive switched systems with time-varying delay, based on the multipleLyapunov technique, a robust resilient guaranteed cost state feedback controller is designedsuch that the corresponding closed-loop system is regular, causal and asymptotically stableand satisfes a cost upper bound. Further, a minimization approach of the largest singularvalue of matrices and a convex optimization method are introduced to seek an optimal robustresilient guaranteed cost controller. All conditions are presented in the form of linear matrixinequalities, and a numerical example is showed to illustrate the correctness of proposedresults.2) Robust resilient control for impulsive switched systems under asynchronous switchingFor impulsive switched systems, through constructing the piecewise Lyapunov function,a robust resilient state feedback controller is designed, which for all admissible uncertainties,guarantees that the corresponding closed system is exponentially stable under asynchronousswitching signals based on the average dwell time method. Then using the linear matrixinequalities technique, the conditions are cast into forms of linear matrix inequalities. Finally,an example is given to illustrate the feasibility of the proposed approach.3) Robust resilient time-delay state feedback control for switched systems with time-varying delay under asynchronous switchingFor switched systems with time-varying delay, combined Lyapunov methods with freeweighting matrices methods, a robust resilient time-delay state feedback controller is de-signed, which makes the corresponding closed systems is exponentially stable under asyn- chronously switched signals, and an estimate of the state trajectory is demonstrated simul-taneously. All the criteria are presented in forms of linear matrix inequalities. Finally, anumerical example and simulation results are given to illustrate the correctness and efec-tiveness of the proposed results.