Hi every body,
What is the grammar mistakes in the below long paragraph?!
"There has been an increasing and considerable interest in designing low and fixed-order controllers,
for example, see Special issue on PID (2006) and references therein. This is mainly due
to the fact that high-order controllers are rarely implemented in practical applications. However,
there are fundamental difficulties inherent to the fixed-order controller design. Many researchers
have attempted to tackle these issues in the last three decades. For example, in Haddad et al.
(1993), a solution based on coupled algebraic Riccati equations (CAREs) has been proposed for
robust stability and performance using fixed-order dynamic controllers. The implicit small gain
guaranteed cost bound is used in Haddad et al. (1997) to address the problem of robust stability
and H2 performance via fixed-order controller design. Development of a mixed-norm H2=L1 controller
synthesis framework via fixed-order dynamic compensation for multi-input/single-output
(MISO) systems has been proposed in Haddad and Kapila (1999). In Doyle et al. (1996), the
Lagrange multiplier method has been proposed to design fixed-order controllers using CAREs
in which the order of controller should be less or equal than the order of plant. In Ghahinet
and Apkarian (1994), Iwasaki and Skelton (1994), the fixed-order controller design problem
has been formulated in a state-space framework as an LMI minimization problem subject to
an additional nonconvex, matrix rank constraint. In Henrion et al. (2003), an LMI formulation
has been developed for fixed-order controller design in a polynomial framework, based on polynomial
positivity conditions. The method can assign the closed-loop poles in a given region of
the complex plane, solving the regional pole assignment problem Chilali and Gahinet (1996).
Nonconvexity of the fixed-order controller design problem can be resolved by choosing a particular
tuning parameter, the so-called central polynomial. In Yang et al. (2007), the problem of designing fixed-order robust H∞ controllers has been considered for linear systems affected
by polytopic uncertainty. The design problem has been formulated as an LMI constraint whose
decision variables are controller parameters. In Khatibi et al. (2008), convex parameterization
of fixed-order robust stabilizing controllers for systems with polytopic uncertainty has been represented
as an LMI using the Kalman-Yakubovich-Popov (KYP) lemma. In Malik et al. (2008),
a linear programming approach has been proposed to the synthesis of fixed-order controllers. In
Fujisaki et al. (2008), a general methodology for designing fixed-order controllers for single-input
single-output (SISO) plants has been proposed using mixed deterministic/randomized methods.
In Jin et al. (2008), for a two-parameter feedback configuration, the problem of finding a fixed
or low-order controller to meet the desired time response specifications has been reduced to the
least square estimation (LSE) in the sense of partial model matching (PMM), which minimizes
a quadratic cost function. In Maruta et al. (2009), it is shown how to obtain a fixed-order controller
satisfying multiple H∞ specifications; but it is not guaranteed that the proposed method
always ends to a solution."
