A necessary and sufficient condition for output feedback stabilizability

Design of Robust Output Affine Quadratic Controller

“…The necessary and sufficient conditions to stabilize the linear continuous time invariant system via static output feedback can be found in Kucera and De Souza [14] and in Vesely [22]. In the above and other papers, the authors basically conclude that despite the availability of many approaches and numerical algorithms the static output feedback problem is still open.…”

“…A real symmetric positive (negative) definite matrix is denoted by P > 0 (P < 0). Much of the notation and terminology follows the references of Kucera and De Souza [14], and Gahinet, Apkarian and Chilali [5].…”

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

“…in [2], [3], [4], [5], while research on SOF stabilization of (certain classes of) nonlinear systems has been increasing in the latest years, especially for nonlinear systems with polynomial vector fields. Recently the interest on polynomial systems has increased dramatically, possibly driven by two main reasons: one is that polynomial systems appear in a wide range of applications, spanning from biology to HVAC control to jet propulsion [6]; the second reason is the recent development of numerical tools based on sum-of-squares (SOS) decomposition for nonlinear analysis and controller synthesis [7].…”

Output Feedback Control of Discrete-time LTI Systems: Scaling LMI Approaches

“…This naturally motivates the employment of output feedback, which only use measurable output in its feedback design. From implementation point of view, static feedback is more cost effective, more reliable and easier to implement than dynamic feedback (Khalil, 2002;Kučera & Souza, 1995;Syrmos et al, 1997). Moreover, many other problems are reducible to some variation of it.…”

“…Although this problem is also known NP-hard (Syrmos et al, 1997), the curious fact to note here is that these early negative results have not prevented researchers from studying output feedback problems. In fact, there are a lot of existing works addressing this problem using different approaches, say, for example, Riccati equation approach, rank-constrained conditions, approach based on structural properties, bilinear matrix inequality (BMI) approaches and min-max optimization techniques (e.g., Bara & Boutayeb (2005;; Benton (Jr.); Gadewadikar et al (2006) ;Geromel, de Oliveira & Hsu (1998) ;Geromel et al (1996); Ghaoui et al (2001); Henrion et al (2005); Kučera & Souza (1995); Syrmos et al (1997) and the references therein). Nevertheless, the LMI approaches for this problem remain popular (Bara & Boutayeb, 2005;Cao & Sun, 1998;Geromel, de Oliveira & Hsu, 1998;Geromel et al, 1996;Prempain & Postlethwaite, 2001;Yu, 2004;Zečević & Šiljak, 2004) due to simplicity and efficiency.…”