In recent years, the study of systems subject to time-varying parameters has awakened the interest of many researchers. The gain scheduling control strategy guarantees a good performance for systems of this type and also is considered as the simplest to deal with problems of this nature. Moreover, the class of systems in which the state derivative signals are easier to obtain than the state signals, such as in the control for reducing vibrations in a mechanical system, has gained an important hole in control theory. Considering those ideas, we propose sufficient conditions via LMI for designing a gain scheduling controller using state derivative feedback. The D-stability methodology was used for improving the performance of the transitory response. Practical implementation in an active suspension system and comparison with other methods validates the efficiency of the proposed strategy.
Este trabalho aborda o problema de estabiliza¸c˜ao de sistemas descritores lineares em tempo cont´ınuo sujeitos a parˆametros variantes no tempo atrav´es de uma realimenta¸c˜ao com ganho escalonado (gain scheduled) da derivada dos estados. O projeto do controlador gain scheduled (GS) ´e obtido por meio de uma condi¸c˜ao de estabilidade descrita em termos de desigualdades matriciais lineares (LMIs) considerando uma fun¸c˜ao de Lyapunov independentedos parˆametros. O Lema de Finsler ´e utilizado para obter condi¸c˜oes de projeto menos conservadoras. Exemplos num´ericos s˜ao apresentados para demonstrar e validar a eficiˆencia da teoria proposta.
This paper addresses the design of state observers for linear discrete-time descriptor systems. Assuming that the original descriptor system is completely observable, an equivalent (standard) state-space representation of the system is proposed which preserves the system observability. Then, an LMI based approach is proposed for designing a Luenberger-like observer. In addition, a separation principle is demonstrated considering the estimation error dynamics and the closed-loop representation of the original descriptor system. Then, the observer design is extended to cope with model disturbances in an H1 sense. The eectiveness of the proposed methodology is illustrated by numerical examples.
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