Informatica

This note presents an indirect adaptive control scheme applicable to nominally controllable non-necessarily inversely stable first-order continuous linear time-invariant systems with unmodelled dynamics. The control objective is to achieve a bounded tracking-error between the system output and a reference signal. A least-squares algorithm with normalization is used to estimate the plant parameters by using two additional design tools, namely: 1) a modification of the parameter estimates and 2) a relative adaptation dead-zone. The modification is based on the properties of the inverse of the least-squares covariance matrix and it uses an hysteresis switching function. In this way, the non-singularity of the controllability matrix of the estimated model of the plant is ensured. The relative dead-zone is used to turn off the adaptation process when an absolute augmented error is smaller than the value of an available overbounding function of the unmodelled dynamics contribution plus, eventually, bounded noise.

For pipelining and block processing in linear time-varying (LTV), linear periodically time-varying (LPTV), and linear time-invariant (LTI) discrete-time systems, we suggest to use the general solution of state space equations. First, we develop three pipelined-block models for LTV, LPTV, and LTI discrete-time systems, and two pipelined-block structures. Afterwards, we analyse complete state controllability, complete output controllability, and complete observability of LTV and LTI pipelined-block discrete-time systems.

This paper discusses the inversion of linear periodically time-varying (LPTV) digital filters using the idea of converting the LPTV filter to the block time-invariant filter. Explicit expressions are given to determine the inversion of LPTV filters. Controllability, observability and stability of the inversion of LPTV filters are discussed.