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.

This paper addresses the study of the controllability and stability of the equilibrium in economic models which relate the unemployment level to the government expenditure. The interesting cases when the government expenditure is either bounded or a linear function of the national income are specifically considered. The relationships between both variables, namely, unemployment growth level and government expenditure is obtained by considering a Keynesian static model for the national income as well as a differential unemployment-inflation model of Phillips type. Both models are used to derive a new combined one by eliminating the common variable “taxes” which is driven by the investment and government expenditure.

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.

In this paper, we propose to present the direct form recursive digital filter as a state space filter. Then, we apply a look-ahead technique and derive a pipelined equation for block output computation. In addition, we study the stability and multiplication complexity of the proposed pipelined-block implementation and compare with complexities of other methods. An algorithm is derived for the iterative computation of pipelined-block matrices.