General dissipative output feedback control for nonlinear systems

L2 - Gain and Passivity Techniques in Nonlinear Control

“…The nonlinear suboptimal 1foo control problem for y ::: 0 is the problem of finding a controller such that the closed-loop system is dissipative with respect to the L2-gain supply rate iy211dll2 -illzl1 2 . This suggests to consider the general dissipative control problem of finding a controller which renders the closed-loop system dissipative with respect to a given supply rate s(d, z); see Yuliar & James,[215], Yuliar, James & Helton,[216], Shishkin & Hill,[184]. This includes the problem of rendering a system passive as treated in Chapter 5.…”

Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

“…Assume R = 1 β I > 0, without loss of generality, where β comes from (21). Thus, (19) implies (23) if…”

“…Dissipative control comprises positive real and H∞ control as particular cases [20]. In article [21], output feedback of smooth nonlinear systems was handled, and state feedback was rather addressed in [22]. The dissipative control problem of LTI plants via linear SOF was addressed in [20] and [23].…”

Robust H∞ PID Controller Design Via LMI Solution of Dissipative Integral Backstepping with State Feedback Synthesis

“…The dissipative method provides a unifying tool as index performances of control systems can be expressed in a general supply rate by selecting values of the supply rate parameters. The general quadratic supply rate function (Hill & Moylan, 1977) is given by the following equation (Hill & Moylan, 1977;Yuliar et al, 1997) (1 )…”

“…Further improvement of the PID controller is sought by applying advanced control designs (Ge et al, 2002;Hara et al, 2006;Wang et al, 2007;Goncalves et al, 2008). In order to design with robust control theory, the PID controller is expressed as a state feedback control law problem that can then be solved by using any full state feedback robust control synthesis, such as Guaranteed Cost Design using Quadratic Bound (Petersen et al, 2000), H ∞ synthesis (Green & Limebeer, 1995;Zhou & Doyle, 1998), Quadratic Dissipative Linear Systems (Yuliar et al, 1997) and so forth. The PID parameters selection by www.intechopen.com Robust Control, Theory and Applications 70 transforming into state feedback using linear quadratic method was first proposed by Williamson and Moore in (Williamson & Moore, 1971).…”