H_? Controller Design For Asynchronous Multi-rate Sampled-data Systems

As the rapid development in computer science,networked control systems have been wide-ly applied in control field.Such systems can enlarge control time and expand control space of traditional systems,achieve economic,effective and efficient results.However,due to the added devices and new control strategy adopted in such system,it also brings great challenge.It is nec-essary to extend and improve the exiting control theories and methods,seek novel control scheme and valid method to deal with new problems.In this paper,the traditional lifting technique has been improved and extended to special systems with new strategy;delays and randomness induced by network are taken into account,and some rigorous derivation and effective approaches are pro-posed;in view of the complexity of multi-rate sampled-data large-scale systems with longitudinal structure constraints,a preliminary method about decentralization control is proposed.The main contents and results in this dissertation are summarized as follows:1.Analysis and synthesis of a linear discrete asynchronous multi-rate sampled-data system are considered.A new definition on asynchronism is given,which conforms to the actual situation.H? controller based on an observer is proposed,which guarantees the stability of the closed system and makes the H? norm of the closed system less than a given attenuation level.To further improve the performance,a tradeoff strategy is applied.That is,the exogenous signals sampled at different rates are lifted to an appropriate signal rate,while the endogenous signals are not lifted to avoid the causal constraint and the dimension multiplied again.The controller is obtained by solving the corresponding matrix inequality,which can be calculated by Matlab.2.Solutions to the H? synthesis problems of asynchronous hybrid systems with input-output delays are proposed.The continuous-time lifting approach of sampled-data systems is extended to a hybrid system with multiple delays,and some feasible formulas to calculate the operators of the equivalent discrete-time(DT)system are given.Different from the exiting methods,which are derived from symplectic pair theory or by state-augmentation,a Lyapunov-Krasovskii functional to analyze the synthesis problem is explicitly constructed.The delay-dependent stability conditions we obtained can be described in terms of LMIs,which are much more convenient to be solved by LMI tools.The static and dynamic output-feedback controller of period and aperiodic systems are obtained respectively,which can stabilize both the equivalent and original system.A rule to choose proper period as the period of the whole system is given,if the system is periodic.The condition obtained before can be extended to the augmented system.3.Solutions to the H? synthesis of stochastic asynchronous discrete-time(DT)networked control systems(NCSs)with two time-delay Markov chains are proposed.Different from the exit-ing methods,another Lyapunov-Krasovskii functional to solve the synthesis problem is explicitly constructed.Both sensor-to-controller(S-C)and controller-to-actuator(C-A)random networked-induced delays are considered and modeled as two separated Markov chains.Moreover,stochastic sampling of S-C and holding of C-A are also considered in the systems for the first time.In view of a specified definition of state with delays and a more rigour inequality,sufficient delay-dependent stability conditions are obtained,which are less conservative and convenient to be solved by LMI tools,due to fewer tuning parameters and lower dimension.Furthermore,the conditions can be transformed LMIs by slack matrix method.4.A decentralized H? control strategy for discrete-time large-scale overlapping systems is proposed.Based on the inclusion principle,the original system is expanded by transforming matrices of longitudinal topology,thus the original system is decomposed.A two-part-controller is constructed to eliminate the perturbation and stabilize the decomposed systems with structure constraint.According to H? theory,a decentralized controller is obtained by the CCLA.If the re?striction condition is also satisfied,the obtained controller can be restricted to stabilize the original system.The method can be extended to systems with uncertainties.