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This work proposes two new approaches based on the ordinary least‐squares method and the total least‐squares method to estimate the parameters of a balanced three‐phase transmission line using voltage and current measurements from phasor measurement unit. First, a new model for the steady‐state phasorial equations of a medium‐length transmission line is proposed. Then, the noises acting upon each measurement on the ordinary least‐squares setup are considered, and for the total least‐squares setup, noise acting upon the observation matrix in order to account for model uncertainties and non‐linearities is also considered. The methods are tested in simulation data of a real medium‐size transmission line.s The main goal is to compare both methods and show their complexities. The results show good performances for both methods and, indeed, the total least‐squares setup had better performance than other reported total least‐squares estimators, which use a different phasorial set of equations and oversimplified noise modelling. It is concluded that for the ordinary least‐squares, the solution is well known and its behavior is predictable. While for the total least‐squares, the solution requires more sophisticated methods of matrix decomposition and its behavior is not as predictable. Therefore the implications of these new approaches, where new considerations about the modelling of the noises are made and where a new phasorial set of equations is used are significant, given that the many works in the literature make use of these common‐place tools. [ABSTRACT FROM AUTHOR]

We revisit the issue of quadratic gain-scheduled and robust state-feedback control with a focus on linear matrix inequalities widely used in the literature. It has been established that for continuous-time linear parameter-varying systems which depend affinely on the scheduling parameter, gain-scheduled stabilisability implies robust stabilisability. In other words, as far as stabilisation is concerned, using a more complex gain-scheduled controller is not advantageous. The proof of such equivalence is non constructive and, although very general, limited to stabilisability. One contribution of the present paper is to establish constructive proofs in the quadratic case that can be extended to performance optimisation in terms of quadratic H 2 and H ∞ norms. One issue investigated in detail is the strategy of using pre-filters to handle parameter-variation in the input matrix. Our results show that said technique, which has been popular since the 1980s, is rarely productive in the sense that solvability of quadratic gain-scheduled control design problems for the original system augmented with an arbitrary pre-filter implies existence of a lower-dimensional quadratic robust controller for the original system, which we construct explicitly via projections. [ABSTRACT FROM AUTHOR]

We introduce new conditions for the H∞ synthesis of discrete-time linear parameter-varying systems in the form of linear matrix inequalities. A distinctive feature of the proposed conditions is the ability to handle variation in both the dynamics and the input matrices without resorting to dynamic augmentation or iterative procedures. We show that this new condition contains the existing poly-quadratic H∞ synthesis result as a particular case. We also derive a corollary which shows improvement even in the stronger case of quadratic H∞ synthesis. Additionally, we show that, surprisingly, a dynamic gain-scheduled quadratic H∞ controller can result in inferior performance compared to a static robust controller. Numerical examples illustrate our results. [ABSTRACT FROM AUTHOR]