Abstract: This paper presents new LMI characterizations for stability, H2 and H∞ norms of discrete-time descriptor systems. Based on these characterizations, an iterative design procedure for multiobjective and structurally constrained feedback control are proposed. The first key idea of the iterative design procedure is embedding the previously designed feedback gain K̂ in the descriptor repres...

For a generalized discrete–time system, possibly improper or polynomial, we give realization based formulas for the H2 optimal output feedback controller, under the same general hypotheses as in the proper case. The solution is provided in term of two descriptor algebraic Riccati equations and features the same elegant simplicity as the standard case.

We analyze the structure of the linear differential and difference operators associated with the necessary optimality conditions of optimal control problems for descriptor systems in continuousand discrete-time. It has been shown in [27] that in continuous-time the associated optimality system is a self-conjugate operator associated with a self-adjoint pair of coefficient matrices and we show t...

In the sequel to [12], we discuss behavioural approach for linear, time-varying, differential algebraic (descriptor) systems with real analytic coefficients. The analysis is “almost global” in the sense that the analysis is not restricted to an interval I ⊂ R but is allowed for the “time axis” R\T, where T is a discrete set of critical points, at which the solution may exhibit a finite escape t...

This presentation is a generalization of 8] from square, regular n-by-n, pencils to singular and rectangular m-by-n pencils. We deene arithmetic-like operations on matrix pencils that are a natural extension of sums, products and quotients of real numbers. The algebra of linear transformations may be regarded as a special case of this pencil arithmetic. The language of linear relations leads to...

This paper considers set-membership estimation for discrete-time linear parameter-varying descriptor systems. Ellipsoid bundle, a new set representation tool combining certain characteristics of ellipsoids and zonotopes, is used to design method the considered We use L? technique estimator parameters in order optimize accuracy. also studies stability problem proposed establishes an offline suff...

this paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space takagi-sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. lyapunov krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear behavior can be found in engineering, management science, econ...